5912:
3601:
42:
5898:
5936:
5924:
1470:). Working with positive real-numbers brings several advantages: If the estimator of a single parameter has a positive variance, then the variance and the Fisher information are both positive real numbers; hence they are members of the convex cone of nonnegative real numbers (whose nonzero members have reciprocals in this same cone).
1147:
proposed an economic theory of scientific experimentation in 1876, which sought to maximize the precision of the estimates. Peirce's optimal allocation immediately improved the accuracy of gravitational experiments and was used for decades by Peirce and his colleagues. In his 1882 published lecture
689:
High-quality statistical software provide a combination of libraries of optimal designs or iterative methods for constructing approximately optimal designs, depending on the model specified and the optimality criterion. Users may use a standard optimality-criterion or may program a custom-made
1092:
on an infinite set of observation-locations. Such optimal probability-measure designs solve a mathematical problem that neglected to specify the cost of observations and experimental runs. Nonetheless, such optimal probability-measure designs can be
861:
to analyze the data, however. Indeed, the "Bayesian" label for probability-based experimental-designs is disliked by some researchers. Alternative terminology for "Bayesian" optimality includes "on-average" optimality or "population" optimality.
1483:(LĂśwner) order. This cone is closed under matrix-matrix addition, under matrix-inversion, and under the multiplication of positive real-numbers and matrices. An exposition of matrix theory and the Loewner-order appears in Pukelsheim.
143:
and is assessed with respect to a statistical criterion, which is related to the variance-matrix of the estimator. Specifying an appropriate model and specifying a suitable criterion function both require understanding of
1160:
Unfortunately practice generally precedes theory, and it is the usual fate of mankind to get things done in some boggling way first, and find out afterward how they could have been done much more easily and perfectly.
1156:
Logic will not undertake to inform you what kind of experiments you ought to make in order best to determine the acceleration of gravity, or the value of the Ohm; but it will tell you how to proceed to form a plan of
1116:
for quadratic models. The KĂ´noâKiefer analysis explains why optimal designs for response-surfaces can have discrete supports, which are very similar as do the less efficient designs that have been traditional in
659:
since the criteria . . . are variance-minimizing criteria, . . . a design that is optimal for a given model using one of the . . . criteria is usually near-optimal for the same model with respect to the other
788:
When scientists wish to test several theories, then a statistician can design an experiment that allows optimal tests between specified models. Such "discrimination experiments" are especially important in the
3123:"On the Standard Deviations of Adjusted and Interpolated Values of an Observed Polynomial Function and its Constants and the Guidance They Give Towards a Proper Choice of the Distribution of the Observations"
1810:
are discussed in
Chapter 18 of the textbook by Atkinson, Donev, and Tobias. More advanced discussions occur in the monograph by Fedorov and Hackl, and the articles by Chaloner and Verdinelli and by DasGupta.
1631:
Iterative methods and approximation algorithms are surveyed in the textbook by
Atkinson, Donev and Tobias and in the monographs of Fedorov (historical) and Pukelsheim, and in the survey article by Gaffke and
1363:"On the standard deviations of adjusted and interpolated values of an observed polynomial function and its constants and the guidance they give towards a proper choice of the distribution of observations"
178:
Designs can be optimized when the design-space is constrained, for example, when the mathematical process-space contains factor-settings that are practically infeasible (e.g. due to safety concerns).
655:
The choice of an appropriate optimality criterion requires some thought, and it is useful to benchmark the performance of designs with respect to several optimality criteria. Cornell writes that
291:
of the variance-matrix is called the "information matrix". Because the variance of the estimator of a parameter vector is a matrix, the problem of "minimizing the variance" is complicated. Using
1695:
An introduction to "universal optimality" appears in the textbook of
Atkinson, Donev, and Tobias. More detailed expositions occur in the advanced textbook of Pukelsheim and the papers of Kiefer.
709:
traditional, optimality-criterion, but can specify a custom criterion. In particular, the practitioner can specify a convex criterion using the maxima of convex optimality-criteria and
1964:
acknowledges Wald's influence and results on many pages â 273 (page 55 in the reprinted volume), 280 (62), 289-291 (71-73), 294 (76), 297 (79), 315 (97) 319 (101) â in this article:
2245:
1302:
The adjective "optimum" (and not "optimal") "is the slightly older form in
English and avoids the construction 'optim(um) + al嫉there is no 'optimalis' in Latin" (page x in
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restriction on the number of experimental runs or replications. Some of these methods are discussed by
Atkinson, Donev and Tobias and in the paper by Hardin and
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5688:
5312:
2520:
2274:
669:
Indeed, there are several classes of designs for which all the traditional optimality-criteria agree, according to the theory of "universal optimality" of
1472:
For several parameters, the covariance-matrices and information-matrices are elements of the convex cone of nonnegative-definite symmetric matrices in a
870:
Scientific experimentation is an iterative process, and statisticians have developed several approaches to the optimal design of sequential experiments.
3953:
929:
are discussed in the textbook by
Atkinson, Donev and Tobias, and in the survey of Gaffke and Heiligers and in the mathematical text of Pukelsheim. The
3500:
1236:
673:. The experience of practitioners like Cornell and the "universal optimality" theory of Kiefer suggest that robustness with respect to changes in the
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Since the optimality criterion of most optimal designs is based on some function of the information matrix, the 'optimality' of a given design is
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2016:
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2461:. Classics in Applied Mathematics. Vol. 50 (republication with errata-list and new preface of Wiley (0-471-61971-X) 1993 ed.).
4552:
3700:
3524:
3083:
117:
5940:
2514:
The textbook by
Atkinson, Donev and Tobias has been used for short courses for industrial practitioners as well as university courses.
936:
The earliest optimal designs were developed to estimate the parameters of regression models with continuous variables, for example, by
5982:
345:
of the information matrix. This criterion results in minimizing the average variance of the estimates of the regression coefficients.
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1926:" in his introduction "Jack Kiefer's Contributions to Experimental Design", which is pages xviiâxxiv in the following volume:
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would be impractical. Prudent statisticians examine the other optimal designs, whose number of experimental runs differ.
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5209:
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1992:
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Shin, Yeonjong; Xiu, Dongbin (2016). "Nonadaptive quasi-optimal points selection for least squares linear regression".
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were surveyed later by S. Zacks. Of course, much work on the optimal design of experiments is related to the theory of
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1968:
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wrote, "the modern theory of optimum design has its roots in the decision theory school of U.S. statistics founded by
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proposed optimal designs for polynomial models in 1918. (Kirstine Smith had been a student of the Danish statistician
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670:
299:; being real-valued functions, these "information criteria" can be maximized. The traditional optimality-criteria are
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80:
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is explained in an on-line textbook for practitioners, which has many illustrations and statistical applications:
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4720:
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of optimal designs is discussed in the textbook of
Atkinson, Donev and Tobias and also in the monograph by Goos.
843:
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210:
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are discussed in the advanced monograph by Shah and Sinha and in the survey-articles by Cheng and by
Majumdar.
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have procedures for optimizing a design according to a user's specification. The experimenter must specify a
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2452:
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Peirce, C. S. (1882), "Introductory
Lecture on the Study of Logic" delivered September 1882, published in
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1996:
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These three advantages (of optimal designs) are documented in the textbook by Atkinson, Donev, and Tobias.
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Optimal designs can accommodate multiple types of factors, such as process, mixture, and discrete factors.
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5774:
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3328:
3307:
3287:
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2209:
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1570:: See an on-line textbook for practitioners, which has many illustrations and statistical applications:
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1006:
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930:
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558:
550:
526:
161:
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98:
76:
64:
31:
5911:
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3600:
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Quality through design: Experimental design, off-line quality control, and Taguchi's contributions
1898:
Zacks, S. (1996) "Adaptive Designs for Parametric Models". In: Ghosh, S. and Rao, C. R., (Eds) (1996).
136:
as an optimal design. In practical terms, optimal experiments can reduce the costs of experimentation.
2160:
optimal designs is discussed by Atkinson, Donev, and Tobias and by Pukelsheim (especially Chapter 12).
5755:
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are discussed by according to Atkinson, Donev, and Tobias (page 165). These authors also discuss the
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710:
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Quality through design: Experimental design, off-line quality control, and Taguchi's contributions
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are discussed in Atkinson, Donev, and Tobias. Mathematically, such results are associated with
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Such benchmarking is discussed in the textbook by Atkinson et al. and in the papers of Kiefer.
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2012:
1948:
1934:
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820:
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design can be either better or worse than a non-optimal design. Therefore, it is important to
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628:
624:
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593:
342:
280:
276:
264:
218:
169:
140:
125:
105:
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This criterion maximizes the discrepancy between two proposed models at the design locations.
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2422:
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In system identification, the following books have chapters on optimal experimental design:
2039:
1858:
1756:
1541:
1510:
1374:
1335:
1316:
Guttorp, P.; Lindgren, G. (2009). "Karl Pearson and the Scandinavian school of statistics".
1026:
990:
956:
900:
798:
794:
751:
714:
596:
for the design and an optimality-criterion before the method can compute an optimal design.
300:
129:
2444:
425:
This criterion maximizes a quantity measuring the mutual column orthogonality of X and the
5764:
5508:
5370:
5297:
4972:
4846:
4819:
4796:
4765:
4392:
4387:
4341:
4071:
3722:
3556:
3486:
3439:
2940:
2649:
2440:
2301:
2222:
The Theory of canonical moments with applications in statistics, probability, and analysis
2114:
1768:
1760:
1742:
1734:
1718:
1480:
1271:
1201:
1040:
1010:
892:
783:
755:
737:
726:
698:
694:
514:, which seeks to minimize the average prediction variance over a set of m specific points.
472:
X(X'X)X'. This has the effect of minimizing the maximum variance of the predicted values.
1575:
1506:
5713:
5708:
4171:
4101:
3747:
3242:
3043:"Gergonne's 1815 paper on the design and analysis of polynomial regression experiments"
2576:
2220:
2153:
1641:
See Kiefer ("Optimum Designs for Fitting Biased Multiresponse Surfaces" pages 289â299).
1455:
1450:
Traditionally, statisticians have evaluated estimators and designs by considering some
1165:
1094:
994:
963:
requires excessive experimental runs when the number of variables exceeds three. Box's
828:
288:
272:
199:
91:
45:
5956:
5870:
5837:
5700:
5661:
5472:
5441:
4905:
4859:
4464:
4166:
3993:
3757:
3752:
3380:
3322:
3257:
3059:
3042:
3029:
3008:
2205:
2189:
2185:
2157:
1473:
1347:
1339:
1098:
790:
549:
of parameters, which are estimated via linear combinations of treatment-means in the
191:
4023:
2575:
are discussed by Bailey and by Bapat. The first chapter of Bapat's book reviews the
90:. The creation of this field of statistics has been credited to Danish statistician
5812:
5745:
5722:
5637:
4967:
4263:
4161:
4096:
4038:
3960:
3915:
3530:
3092:
Peirce, C. S. (JulyâAugust 1967). "Note on the Theory of the Economy of Research".
2731:
2579:
used by Bailey (or the advanced books below). Bailey's exercises and discussion of
2360:
2107:
1923:
1842:
1467:
1266:
1173:
908:
888:
802:
640:
48:
developed the optimal design of experiments, and so minimized surveyors' need for
3009:"The application of the method of least squares to the interpolation of sequences"
2371:. Springer-Verlag and the Institute of Mathematical Statistics. pp. 718+xxv.
2342:
2760:
2484:. Lecture Notes in Statistics. Vol. 54. Springer-Verlag. pp. 171+viii.
831:
of such an experiment. Such probability-based optimal-designs are called optimal
5855:
5817:
5500:
5401:
5263:
5076:
5043:
4535:
4452:
4447:
4091:
4048:
4028:
4008:
3998:
3767:
3386:
3317:
3302:
3272:
2964:
1463:
1069:
1018:
426:
380:
222:
17:
732:
allows the practitioner to verify that a given design is globally optimal. The
4701:
4181:
3881:
3812:
3762:
3737:
3657:
3202:
2456:
1863:
1846:
1704:
Computational methods are discussed by Pukelsheim and by Gaffke and Heiligers.
1084:
In the mathematical theory on optimal experiments, an optimal design can be a
585:
469:
411:
312:
214:
206:
49:
27:
Experimental design that is optimal with respect to some statistical criterion
2988:
1553:
1545:
4854:
4706:
4326:
4121:
4033:
4018:
4013:
3978:
3334:
2840:
2781:
Republication with errata-list and new preface of Wiley (0-471-61971-X) 1993
2427:
2410:
1815:
and other aspects of "model-robust" designs are discussed by Chang and Notz.
1789:
Boyd and Vandenberghe discuss optimal experimental designs on pages 384â396.
1672:
Experiments with Mixtures: Designs, Models, and the Analysis of Mixture Data
1605:
Boyd and Vandenberghe discuss optimal experimental designs on pages 384â396.
268:
225:
56:
2976:
Memoirs of the Faculty of Science. Kyushu University. Series A. Mathematics
2592:
2025:
Optimal designs for "follow-up" experiments are discussed by Wu and Hamada.
697:, and therefore optimal-designs are amenable to the mathematical theory of
3105:
2583:
both emphasize statistical concepts (rather than algebraic computations).
1779:
4370:
3988:
3865:
3860:
3855:
3827:
465:
195:
3153:
5875:
5576:
3146:
2436:
1872:
1530:"The design of experiments for discriminating between two rival models"
1514:
1386:
3113:
2369:
Jack Carl Kiefer: Collected papers IIIâDesign of experiments
1660:
designs (including "Bayesian" designs) are surveyed by Chang and Notz.
1005:. Much of this research has been associated with the subdiscipline of
577:
Catalogs of optimal designs occur in books and in software libraries.
5797:
4778:
4752:
4732:
3983:
3774:
959:. However, Box's designs have few optimality properties. Indeed, the
940:
in 1815 (Stigler). In English, two early contributions were made by
3138:
3122:
1378:
1362:
967:
require more experimental runs than do the optimal designs of KĂ´no.
41:
295:, statisticians compress the information-matrix using real-valued
2127:
Stochastic Approximation and Recursive Algorithms and Applications
2070:
Dynamic System Identification: Experiment Design and Data Analysis
2009:
Experiments: Planning, Analysis, and Parameter Design Optimization
985:
The optimization of sequential experimentation is studied also in
677:
is much greater than is robustness with respect to changes in the
40:
2510:
Textbooks emphasizing regression and response-surface methodology
2211:
Tchebycheff systems: With applications in analysis and statistics
1566:
The above optimality-criteria are convex functions on domains of
1104:
In some cases, a finite set of observation-locations suffices to
1064:
There are several methods of finding an optimal design, given an
561:. Statisticians can use appropriate optimality-criteria for such
3717:
2930:
Majumdar, D. "Optimal and Efficient Treatment-Control Designs".
537:
In many applications, the statistician is most concerned with a
379:, which seeks to minimize |(X'X)|, or equivalently maximize the
168:
Optimal designs reduce the costs of experimentation by allowing
5686:
5253:
5000:
4299:
4069:
3686:
3630:
3157:
2609:
Draft available on-line. (Especially Chapter 11.8 "Optimality")
307:
matrix; algebraically, the traditional optimality-criteria are
187:
Experimental designs are evaluated using statistical criteria.
2336:. Lecture Notes in Statistics. Vol. 125. Springer-Verlag.
3626:
446:
Other optimality-criteria are concerned with the variance of
387:
X'X of the design. This criterion results in maximizing the
2737:
Jack Carl Kiefer Collected Papers III Design of Experiments
2106:
Some step-size rules for of Judin & Nemirovskii and of
1940:
Jack Carl Kiefer Collected Papers III Design of Experiments
491:, which seeks to minimize the average prediction variance
2091:
Identification of Parametric Models from Experimental Data
1152:, Peirce introduced experimental design with these words:
360:
of a predetermined linear combination of model parameters.
3071:(1876). "Note on the Theory of the Economy of Research".
1724:
is discussed in Chapter 9 of Atkinson, Donev, and Tobias.
2909:
Gaffke, N. & Heiligers, B. "Approximate Designs for
2697:
The Optimal Design of Blocked and Split-plot Experiments
2631:(Chapter 5 "Block designs and optimality", pages 99â111)
2344:
The Optimal Design of Blocked and Split-plot Experiments
1108:
an optimal design. Such a result was proved by KĂ´no and
1017:
has described methods that are more efficient than the (
827:
on the models and then select any design maximizing the
713:
of optimality criteria (since these operations preserve
160:
Optimal designs offer three advantages over sub-optimal
2856:. Handbook of Statistics. Vol. 13. North-Holland.
2347:. Lecture Notes in Statistics. Vol. 164. Springer.
895:
wrote an overview of optimal sequential designs, while
2811:
Chaloner, Kathryn & Verdinelli, Isabella (1995).
2519:
Atkinson, A. C.; Donev, A. N.; Tobias, R. D. (2007).
2273:
Atkinson, A. C.; Donev, A. N.; Tobias, R. D. (2007).
1937:; Olkin, Ingram; Jerome Sacks; Wynn, Henry P (eds.).
701:
and their computation can use specialized methods of
5539:
Autoregressive conditional heteroskedasticity (ARCH)
2952:
Zacks, S. "Adaptive Designs for Parametric Models".
2706:
Optimal design of experiments: a case study approach
2643:
Books for professional statisticians and researchers
2260:
v. 1, pp. 210â14, see 210â1, also lower down on 211.
2241:, v. 2, n. 19, pp. 11â12, November 1882, see p. 11,
1072:. Of course, fixing the number of experimental runs
604:
Some advanced topics in optimal design require more
120:. A non-optimal design requires a greater number of
5846:
5783:
5736:
5699:
5654:
5636:
5603:
5594:
5552:
5499:
5460:
5409:
5400:
5321:
5278:
5208:
5174:
5128:
5095:
5057:
5024:
4936:
4845:
4764:
4719:
4687:
4640:
4585:
4511:
4502:
4312:
4254:
4228:
4180:
4135:
4082:
3969:
3924:
3898:
3880:
3836:
3788:
3708:
3699:
3453:
3348:
3281:
3191:
464:, which seeks to minimize the maximum entry in the
240:" for that estimator. Because of this reciprocity,
2308:. Society for Industrial and Applied Mathematics.
2156:of optimal probability-measure designs to provide
2117:are explained in the textbook by Kushner and Yin:
2067:Goodwin, Graham C. & Payne, Robert L. (1977).
1973:Journal of the Royal Statistical Society, Series B
1902:Handbook of Statistics, Volume 13. North-Holland.
971:System identification and stochastic approximation
769:and verifying its optimality often are difficult.
608:and practical knowledge in designing experiments.
2219:Dette, Holger & Studden, William J. (1997).
685:Flexible optimality criteria and convex analysis
5087:Multivariate adaptive regression splines (MARS)
1798:See Chapter 20 in Atkinison, Donev, and Tobias.
1574:Boyd, Stephen P.; Vandenberghe, Lieven (2004).
1462:), usually with positive real values (like the
693:All of the traditional optimality-criteria are
657:
651:Choosing an optimality criterion and robustness
2767:Society for Industrial and Applied Mathematics
2463:Society for Industrial and Applied Mathematics
1832:optimality" is advocated in Fedorov and Hackl.
3642:
3169:
2965:"Optimum designs for quadratic regression on
2934:. Handbook of Statistics. pp. 1007â1054.
2925:. Handbook of Statistics. pp. 1149â1199.
2904:. Handbook of Statistics. pp. 1099â1148.
2887:Cheng, C.-S. "Optimal Design: Exact Theory".
2882:. Handbook of Statistics. pp. 1055â1099.
2785:Shah, Kirti R. & Sinha, Bikas K. (1989).
2528:. Oxford University Press. pp. 511+xvi.
2480:Shah, Kirti R. & Sinha, Bikas K. (1989).
2181:, "Markov systems", and "moment spaces": See
2007:Wu, C. F. Jeff & Hamada, Michael (2002).
819:When practitioners need to consider multiple
643:the performance of designs under alternative
487:A second criterion on prediction variance is
172:to be estimated with fewer experimental runs.
8:
2891:. Handbook of Statistics. pp. 977â1006.
1847:"Sequential Tests of Statistical Hypotheses"
1622:are discussed by Atkinson, Donev and Tobias.
510:A third criterion on prediction variance is
55:, while trapped in his tent in storm-ridden
34:. For optimal design in control theory, see
2956:. Handbook of Statistics. pp. 151â180.
1129:In 1815, an article on optimal designs for
627:, its performance may deteriorate on other
623:: While an optimal design is best for that
356:This criterion minimizes the variance of a
5696:
5683:
5600:
5406:
5275:
5250:
5021:
4997:
4725:
4508:
4309:
4296:
4079:
4066:
3705:
3696:
3683:
3649:
3635:
3627:
3176:
3162:
3154:
3085:Collected Papers of Charles Sanders Peirce
2686:Fedorov, Valerii V.; Hackl, Peter (1997).
2332:Fedorov, Valerii V.; Hackl, Peter (1997).
1055:Specifying the number of experimental runs
139:The optimality of a design depends on the
3058:
3028:
3023:from the 1815 French ed.): 439â447.
2987:
2947:. Handbook of Statistics. pp. 63â90.
2830:
2704:Goos, Peter & Jones, Bradley (2011).
2426:
2088:Walter, Ăric & Pronzato, Luc (1997).
1862:
1329:
1290:
773:Model uncertainty and Bayesian approaches
545:. More generally, statisticians consider
2813:"Bayesian Experimental Design: A Review"
2505:Textbooks for practitioners and students
1971:(1959). "Optimum Experimental Designs".
1773:symmetric positive-semidefinite matrices
1568:symmetric positive-semidefinite matrices
1528:Atkinson, A. C.; Fedorov, V. V. (1975).
1080:Discretizing probability-measure designs
1887:Sequential Analysis and Optimal Design,
1283:
5613:KaplanâMeier estimator (product limit)
3019:(4) (Translated by Ralph St. John and
2734:; Jerome Sacks; Wynn, Henry P (eds.).
2655:Sequential Analysis and Optimal Design
2306:Sequential analysis and optimal design
2003:is noted by Wu and Hamada (page 422).
1304:Optimum Experimental Designs, with SAS
1237:Hadamard's maximal determinant problem
1060:Using a computer to find a good design
557:; such linear combinations are called
2411:"The life and work of Gustav Elfving"
2394:. Oxford U. P. pp. 464+xi.
2192:(1953). "Geometry of moment spaces".
1851:The Annals of Mathematical Statistics
183:Minimizing the variance of estimators
7:
5923:
5623:Accelerated failure time (AFT) model
2742:Institute of Mathematical Statistics
2688:Model-Oriented Design of Experiments
2334:Model-Oriented Design of Experiments
2256:v. 4, pp. 378â82, see 378, 379, and
2252:v. 7, paragraphs 59â76, see 59, 63,
1945:Institute of Mathematical Statistics
1495:SIAM Journal on Scientific Computing
1013:, D. Judin & A. Nemirovskii and
951:Pioneering designs for multivariate
857:does not force statisticians to use
5935:
5218:Analysis of variance (ANOVA, anova)
3525:Generalized randomized block design
2567:Textbooks emphasizing block designs
2522:Optimum experimental designs, with
2276:Optimum experimental designs, with
2050:of KĂ´no-type designs for quadratic
1900:Design and Analysis of Experiments,
1784:. Cambridge University Press. 2004.
705:. The practitioner need not select
391:content of the parameter estimates.
5313:CochranâMantelâHaenszel statistics
3939:Pearson product-moment correlation
2954:Design and Analysis of Experiments
2945:Design and Analysis of Experiments
2932:Design and Analysis of Experiments
2923:Design and Analysis of Experiments
2902:Design and Analysis of Experiments
2889:Design and Analysis of Experiments
2880:Design and Analysis of Experiments
2854:Design and Analysis of Experiments
2239:Johns Hopkins University Circulars
1306:, by Atkinson, Donev, and Tobias).
25:
3576:Sequential probability ratio test
2789:. Vol. 54. Springer-Verlag.
2708:. Chichester Wiley. p. 304.
2690:. Vol. 125. Springer-Verlag.
2594:Design of Comparative Experiments
761:If an optimality-criterion lacks
5934:
5922:
5910:
5897:
5896:
3599:
3501:Polynomial and rational modeling
2896:DasGupta, A. "Review of Optimal
2616:Linear Algebra and Linear Models
2551:. Oxford U. P. pp. 464+xi.
2169:Regarding designs for quadratic
1340:10.1111/j.1751-5823.2009.00069.x
1318:International Statistical Review
1049:Handbook of Experimental Designs
389:differential Shannon information
275:of the parameter-estimator is a
5572:Least-squares spectral analysis
2409:NordstrĂśm, Kenneth (May 1999).
1454:of the covariance matrix (of a
1232:Glossary of experimental design
846:(where the response follows an
612:Model dependence and robustness
4553:Mean-unbiased minimum-variance
3268:Replication versus subsampling
2759:Pukelsheim, Friedrich (2006).
2208:; Studden, William J. (1966).
1583:. Cambridge University Press.
410:, which maximizes the minimum
358:best linear unbiased estimator
337:, which seeks to minimize the
30:This article is about optimal
1:
5866:Geographic information system
5082:Simultaneous equations models
2762:Optimal Design of Experiments
2679:Theory of Optimal Experiments
2619:(Second ed.). Springer.
2458:Optimal design of experiments
2325:Theory of Optimal Experiments
2254:Writings of Charles S. Peirce
2130:(Second ed.). Springer.
1051:chapter by Shelemyahu Zacks.
695:convex (or concave) functions
209:(under the conditions of the
148:and practical knowledge with
5049:Coefficient of determination
4660:Uniformly most powerful test
3495:Response surface methodology
3403:Analysis of variance (Anova)
3060:10.1016/0315-0860(74)90033-0
3030:10.1016/0315-0860(74)90034-2
2225:. John Wiley & Sons Inc.
1993:response surface methodology
1437:are fundamental concepts in
1257:Response surface methodology
1222:Entropy (information theory)
1187:Bayesian experimental design
1119:response surface methodology
1031:response-surface methodology
921:Response surface methodology
915:Response-surface methodology
815:Bayesian experimental design
809:Bayesian experimental design
69:optimal experimental designs
5998:Statistical process control
5618:Proportional hazards models
5562:Spectral density estimation
5544:Vector autoregression (VAR)
4978:Maximum posterior estimator
4210:Randomized controlled trial
3565:Randomized controlled trial
3090:paragraphs 139â157, and in
2044:"central-composite" designs
965:"central-composite" designs
905:statistical decision theory
315:of the information matrix.
236:) estimator is called the "
6019:
5378:Multivariate distributions
3798:Average absolute deviation
2740:. Springer-Verlag and the
2699:. Vol. 164. Springer.
2173:, the results of KĂ´no and
1943:. Springer-Verlag and the
997:. Popular methods include
974:
918:
877:
812:
781:
530:
524:
429:of the information matrix.
414:of the information matrix.
29:
5983:Mathematical optimization
5892:
5695:
5682:
5366:Structural equation model
5274:
5249:
5020:
4996:
4728:
4702:Score/Lagrange multiplier
4308:
4295:
4117:Sample size determination
4078:
4065:
3695:
3682:
3664:
3584:
2787:Theory of Optimal Designs
2482:Theory of Optimal Designs
2124:; Yin, G. George (2003).
1674:(third ed.). Wiley.
1408:Such criteria are called
866:Iterative experimentation
844:generalized linear models
721:optimality criteria, the
5861:Environmental statistics
5383:Elliptical distributions
5176:Generalized linear model
5105:Simple linear regression
4875:HodgesâLehmann estimator
4332:Probability distribution
4241:Stochastic approximation
3803:Coefficient of variation
3551:Repeated measures design
3263:Restricted randomization
3121:Smith, Kirstine (1918).
2989:10.2206/kyushumfs.16.114
1616:"parameters of interest"
1614:Optimality criteria for
1361:Smith, Kirstine (1918).
1252:Replication (statistics)
1150:Johns Hopkins University
1114:response-surface designs
999:stochastic approximation
981:Stochastic approximation
842:are used especially for
801:, following the work of
711:nonnegative combinations
600:Practical considerations
194:estimator minimizes the
5521:Cross-correlation (XCF)
5129:Non-standard predictors
4563:LehmannâScheffĂŠ theorem
4236:Adaptive clinical trial
2963:KĂ´no, Kazumasa (1962).
2677:Fedorov, V. V. (1972).
2323:Fedorov, V. V. (1972).
2284:Oxford University Press
1864:10.1214/aoms/1177731118
1217:Efficiency (statistics)
1003:stochastic optimization
927:response-surface models
539:"parameter of interest"
460:A popular criterion is
375:A popular criterion is
232:of the variance of an (
112:allow parameters to be
50:theodolite measurements
6003:Management cybernetics
5988:Industrial engineering
5917:Mathematics portal
5738:Engineering statistics
5646:NelsonâAalen estimator
5223:Analysis of covariance
5110:Ordinary least squares
5034:Pearson product-moment
4438:Statistical functional
4349:Empirical distribution
4182:Controlled experiments
3911:Frequency distribution
3689:Descriptive statistics
3606:Mathematics portal
3368:Ordinary least squares
2465:. pp. 454+xxxii.
2367:; et al. (eds.).
2353:Kiefer, Jack Carl
1824:As an alternative to "
1670:Cornell, John (2002).
1546:10.1093/biomet/62.1.57
1163:
987:stochastic programming
667:
563:parameters of interest
114:estimated without bias
60:
5963:Design of experiments
5833:Population statistics
5775:System identification
5509:Autocorrelation (ACF)
5437:Exponential smoothing
5351:Discriminant analysis
5346:Canonical correlation
5210:Partition of variance
5072:Regression validation
4916:(JonckheereâTerpstra)
4815:Likelihood-ratio test
4504:Frequentist inference
4416:Locationâscale family
4337:Sampling distribution
4302:Statistical inference
4269:Cross-sectional study
4256:Observational studies
4215:Randomized experiment
4044:Stem-and-leaf display
3846:Central limit theorem
3203:Scientific experiment
3185:Design of experiments
3106:10.1287/opre.15.4.643
2939:Stufken, J. "Optimal
2911:Polynomial Regression
2841:10.1214/ss/1177009939
2805:Articles and chapters
2613:Bapat, R. B. (2000).
2453:Pukelsheim, Friedrich
2428:10.1214/ss/1009212244
2214:. Wiley-Interscience.
2179:Chebyshev polynomials
1212:Design of experiments
1192:Blocking (statistics)
1172:and was working with
1154:
1131:polynomial regression
1007:system identification
1001:and other methods of
977:System identification
823:, they can specify a
551:design of experiments
543:"nuisance parameters"
527:Contrast (statistics)
493:over the design space
190:It is known that the
150:designing experiments
99:design of experiments
83:with respect to some
65:design of experiments
44:
32:design of experiments
5756:Probabilistic design
5341:Principal components
5184:Exponential families
5136:Nonlinear regression
5115:General linear model
5077:Mixed effects models
5067:Errors and residuals
5044:Confounding variable
4946:Bayesian probability
4924:Van der Waerden test
4914:Ordered alternative
4679:Multiple comparisons
4558:RaoâBlackwellization
4521:Estimating equations
4477:Statistical distance
4195:Factorial experiment
3728:Arithmetic-Geometric
3477:Fractional factorial
3088:. Vol. 7. 1958.
3047:Historia Mathematica
3013:Historia Mathematica
2695:Goos, Peter (2002).
2341:Goos, Peter (2002).
2286:. pp. 511+xvi.
2258:The Essential Peirce
2194:Mem. Amer. Math. Soc
1947:. pp. 718+xxv.
1885:Chernoff, H. (1972)
1477:ordered vector space
1135:Joseph Diaz Gergonne
1047:are surveyed in the
925:Optimal designs for
743:is related with the
675:optimality-criterion
555:analysis of variance
211:GaussâMarkov theorem
162:experimental designs
77:experimental designs
5993:Systems engineering
5968:Regression analysis
5828:Official statistics
5751:Methods engineering
5432:Seasonal adjustment
5200:Poisson regressions
5120:Bayesian regression
5059:Regression analysis
5039:Partial correlation
5011:Regression analysis
4610:Prediction interval
4605:Likelihood interval
4595:Confidence interval
4587:Interval estimation
4548:Unbiased estimators
4366:Model specification
4246:Up-and-down designs
3934:Partial correlation
3890:Index of dispersion
3808:Interquartile range
3611:Statistical outline
3571:Sequential analysis
3536:Graeco-Latin square
3445:Multiple comparison
3392:Hierarchical model:
3094:Operations Research
3077:(Appendix No. 14).
3073:Coast Survey Report
3039:Stigler, Stephen M.
2921:, and Optimality".
2818:Statistical Science
2415:Statistical Science
1781:Convex Optimization
1748:in relation to the
1746:equivalence theorem
1722:equivalence theorem
1577:Convex Optimization
1507:2016SJSC...38A.385S
1414:optimization theory
1410:objective functions
1207:Convex minimization
1197:Computer experiment
1086:probability measure
1009:. In computational
885:Sequential analysis
880:Sequential analysis
874:Sequential analysis
825:probability-measure
741:equivalence theorem
730:equivalence theorem
703:convex minimization
582:statistical systems
580:In addition, major
547:linear combinations
5973:Statistical theory
5848:Spatial statistics
5728:Medical statistics
5628:First hitting time
5582:Whittle likelihood
5233:Degrees of freedom
5228:Multivariate ANOVA
5161:Heteroscedasticity
4973:Bayesian estimator
4938:Bayesian inference
4787:KolmogorovâSmirnov
4672:Randomization test
4642:Testing hypotheses
4615:Tolerance interval
4526:Maximum likelihood
4421:Exponential family
4354:Density estimation
4314:Statistical theory
4274:Natural experiment
4220:Scientific control
4137:Survey methodology
3823:Standard deviation
3616:Statistical topics
3208:Statistical design
3007:(November 1974) .
2728:Brown, Lawrence D.
2597:. Cambridge U. P.
2122:Kushner, Harold J.
2113:2007-10-31 at the
2073:. Academic Press.
2001:BoxâBehnken design
1935:Brown, Lawrence D.
1910:. (pages 151â180)
1515:10.1137/15M1015868
1460:unbiased estimator
1439:statistical theory
1427:Fisher information
1242:Information theory
1227:Fisher information
1170:Thorvald N. Thiele
1112:in their works on
961:BoxâBehnken design
848:exponential-family
606:statistical theory
533:Nuisance parameter
406:Another design is
385:information matrix
297:summary statistics
293:statistical theory
238:Fisher information
219:statistical models
170:statistical models
146:statistical theory
106:statistical models
61:
36:shape optimization
5978:Optimal decisions
5950:
5949:
5888:
5887:
5884:
5883:
5823:National accounts
5793:Actuarial science
5785:Social statistics
5678:
5677:
5674:
5673:
5670:
5669:
5605:Survival function
5590:
5589:
5452:Granger causality
5293:Contingency table
5268:Survival analysis
5245:
5244:
5241:
5240:
5097:Linear regression
4992:
4991:
4988:
4987:
4963:Credible interval
4932:
4931:
4715:
4714:
4531:Method of moments
4400:Parametric family
4361:Statistical model
4291:
4290:
4287:
4286:
4205:Random assignment
4127:Statistical power
4061:
4060:
4057:
4056:
3906:Contingency table
3876:
3875:
3743:Generalized/power
3624:
3623:
3511:Central composite
3409:Cochran's theorem
3363:Linear regression
3340:Nuisance variable
3253:Random assignment
3230:Experimental unit
3041:(November 1974).
2941:Crossover Designs
2863:978-0-444-82061-7
2796:978-0-387-96991-6
2776:978-0-89871-604-7
2751:978-0-387-96004-3
2724:Kiefer, Jack Carl
2715:978-0-470-74461-1
2681:. Academic Press.
2669:978-0-89871-006-9
2626:978-0-387-98871-9
2604:978-0-521-68357-9
2558:978-0-19-851993-5
2535:978-0-19-929660-6
2491:978-0-387-96991-6
2472:978-0-89871-604-7
2401:978-0-19-851993-5
2378:978-0-387-96004-3
2327:. Academic Press.
2315:978-0-89871-006-9
2293:978-0-19-929660-6
2171:response-surfaces
2137:978-0-387-00894-3
2080:978-0-12-289750-4
2052:response-surfaces
2018:978-0-471-25511-6
1954:978-0-387-96004-3
1931:Kiefer, Jack Carl
1681:978-0-471-07916-3
1590:978-0-521-83378-3
1452:summary statistic
1262:Statistical model
1145:Charles S. Peirce
1133:was published by
1101:optimal designs.
955:were proposed by
953:response-surfaces
942:Charles S. Peirce
903:, especially the
901:optimal decisions
887:was pioneered by
765:, then finding a
541:rather than with
333:One criterion is
265:statistical model
141:statistical model
122:experimental runs
75:) are a class of
16:(Redirected from
6010:
5938:
5937:
5926:
5925:
5915:
5914:
5900:
5899:
5803:Crime statistics
5697:
5684:
5601:
5567:Fourier analysis
5554:Frequency domain
5534:
5481:
5447:Structural break
5407:
5356:Cluster analysis
5303:Log-linear model
5276:
5251:
5192:
5166:Homoscedasticity
5022:
4998:
4917:
4909:
4901:
4900:(KruskalâWallis)
4885:
4870:
4825:Cross validation
4810:
4792:AndersonâDarling
4739:
4726:
4697:Likelihood-ratio
4689:Parametric tests
4667:Permutation test
4650:1- & 2-tails
4541:Minimum distance
4513:Point estimation
4509:
4460:Optimal decision
4411:
4310:
4297:
4279:Quasi-experiment
4229:Adaptive designs
4080:
4067:
3944:Rank correlation
3706:
3697:
3684:
3651:
3644:
3637:
3628:
3604:
3603:
3541:Orthogonal array
3178:
3171:
3164:
3155:
3150:
3117:
3089:
3076:
3064:
3062:
3034:
3032:
2993:
2991:
2973:
2957:
2948:
2935:
2926:
2905:
2898:Bayesian Designs
2892:
2883:
2867:
2844:
2834:
2800:
2780:
2765:. Vol. 50.
2755:
2719:
2700:
2691:
2682:
2673:
2650:Chernoff, Herman
2630:
2608:
2562:
2543:Logothetis, N.;
2539:
2495:
2476:
2448:
2430:
2405:
2388:Wynn, H. P.
2386:Logothetis, N.;
2382:
2348:
2337:
2328:
2319:
2302:Chernoff, Herman
2297:
2261:
2250:Collected Papers
2235:
2229:
2226:
2215:
2201:
2167:
2161:
2150:
2144:
2141:
2104:
2098:
2095:
2084:
2061:
2055:
2032:
2026:
2022:
1991:In the field of
1989:
1983:
1980:
1958:
1917:
1911:
1896:
1890:
1883:
1877:
1876:
1866:
1839:
1833:
1822:
1816:
1813:Bayesian designs
1808:Bayesian designs
1805:
1799:
1796:
1790:
1785:
1769:convex functions
1761:convex functions
1733:Pukelsheim uses
1731:
1725:
1711:
1705:
1702:
1696:
1693:
1687:
1685:
1667:
1661:
1648:
1642:
1639:
1633:
1629:
1623:
1612:
1606:
1601:
1599:
1597:
1582:
1564:
1558:
1557:
1525:
1519:
1518:
1501:(1): A385âA411.
1490:
1484:
1448:
1442:
1423:
1417:
1406:
1400:
1397:
1391:
1390:
1358:
1352:
1351:
1333:
1313:
1307:
1300:
1294:
1288:
1272:Wolfowitz, Jacob
1157:experimentation.
1045:adaptive designs
1037:Adaptive designs
957:George E. P. Box
897:adaptive designs
859:Bayesian methods
840:Bayesian designs
799:pharmacodynamics
795:pharmacokinetics
756:convex functions
715:convex functions
665:
118:minimum variance
21:
18:D-optimal design
6018:
6017:
6013:
6012:
6011:
6009:
6008:
6007:
5953:
5952:
5951:
5946:
5909:
5880:
5842:
5779:
5765:quality control
5732:
5714:Clinical trials
5691:
5666:
5650:
5638:Hazard function
5632:
5586:
5548:
5532:
5495:
5491:BreuschâGodfrey
5479:
5456:
5396:
5371:Factor analysis
5317:
5298:Graphical model
5270:
5237:
5204:
5190:
5170:
5124:
5091:
5053:
5016:
5015:
4984:
4928:
4915:
4907:
4899:
4883:
4868:
4847:Rank statistics
4841:
4820:Model selection
4808:
4766:Goodness of fit
4760:
4737:
4711:
4683:
4636:
4581:
4570:Median unbiased
4498:
4409:
4342:Order statistic
4304:
4283:
4250:
4224:
4176:
4131:
4074:
4072:Data collection
4053:
3965:
3920:
3894:
3872:
3832:
3784:
3701:Continuous data
3691:
3678:
3660:
3655:
3625:
3620:
3598:
3580:
3557:Crossover study
3548:
3546:Latin hypercube
3482:PlackettâBurman
3461:
3458:
3457:
3449:
3352:
3344:
3285:
3277:
3194:
3187:
3182:
3139:10.2307/2331929
3120:
3091:
3082:
3081:. Reprinted in
3079:NOAA PDF Eprint
3067:
3037:
3005:Gergonne, J. D.
3003:
3000:
2971:
2962:
2951:
2938:
2929:
2908:
2895:
2886:
2870:
2864:
2852:, eds. (1996).
2847:
2810:
2807:
2797:
2784:
2777:
2758:
2752:
2722:
2716:
2703:
2694:
2685:
2676:
2670:
2648:
2645:
2627:
2612:
2605:
2587:
2569:
2559:
2542:
2536:
2518:
2512:
2507:
2502:
2500:Further reading
2492:
2479:
2473:
2451:
2408:
2402:
2385:
2379:
2351:
2340:
2331:
2322:
2316:
2300:
2294:
2272:
2269:
2264:
2248:. Reprinted in
2236:
2232:
2218:
2204:
2184:
2168:
2164:
2151:
2147:
2138:
2120:
2115:Wayback Machine
2105:
2101:
2087:
2081:
2066:
2062:
2058:
2033:
2029:
2019:
2006:
1990:
1986:
1967:
1955:
1929:
1918:
1914:
1897:
1893:
1889:SIAM Monograph.
1884:
1880:
1841:
1840:
1836:
1823:
1819:
1806:
1802:
1797:
1793:
1778:
1735:convex analysis
1732:
1728:
1712:
1708:
1703:
1699:
1694:
1690:
1686:(Pages 400-401)
1682:
1669:
1668:
1664:
1649:
1645:
1640:
1636:
1630:
1626:
1613:
1609:
1595:
1593:
1591:
1580:
1573:
1565:
1561:
1527:
1526:
1522:
1492:
1491:
1487:
1471:
1449:
1445:
1424:
1420:
1407:
1403:
1398:
1394:
1379:10.2307/2331929
1360:
1359:
1355:
1331:10.1.1.368.8328
1315:
1314:
1310:
1301:
1297:
1291:NordstrĂśm (1999
1289:
1285:
1281:
1276:
1202:Convex function
1182:
1159:
1158:
1137:, according to
1127:
1082:
1062:
1057:
1041:clinical trials
1023:step-size rules
1011:optimal control
983:
973:
923:
917:
893:Herman Chernoff
882:
876:
868:
855:Bayesian design
850:distribution).
817:
811:
786:
784:Model selection
780:
778:Model selection
775:
699:convex analysis
687:
666:
664:
653:
614:
602:
575:
535:
529:
523:
271:, however, the
250:corresponds to
185:
158:
110:optimal designs
73:optimum designs
39:
28:
23:
22:
15:
12:
11:
5:
6016:
6014:
6006:
6005:
6000:
5995:
5990:
5985:
5980:
5975:
5970:
5965:
5955:
5954:
5948:
5947:
5945:
5944:
5932:
5920:
5906:
5893:
5890:
5889:
5886:
5885:
5882:
5881:
5879:
5878:
5873:
5868:
5863:
5858:
5852:
5850:
5844:
5843:
5841:
5840:
5835:
5830:
5825:
5820:
5815:
5810:
5805:
5800:
5795:
5789:
5787:
5781:
5780:
5778:
5777:
5772:
5767:
5758:
5753:
5748:
5742:
5740:
5734:
5733:
5731:
5730:
5725:
5720:
5711:
5709:Bioinformatics
5705:
5703:
5693:
5692:
5687:
5680:
5679:
5676:
5675:
5672:
5671:
5668:
5667:
5665:
5664:
5658:
5656:
5652:
5651:
5649:
5648:
5642:
5640:
5634:
5633:
5631:
5630:
5625:
5620:
5615:
5609:
5607:
5598:
5592:
5591:
5588:
5587:
5585:
5584:
5579:
5574:
5569:
5564:
5558:
5556:
5550:
5549:
5547:
5546:
5541:
5536:
5528:
5523:
5518:
5517:
5516:
5514:partial (PACF)
5505:
5503:
5497:
5496:
5494:
5493:
5488:
5483:
5475:
5470:
5464:
5462:
5461:Specific tests
5458:
5457:
5455:
5454:
5449:
5444:
5439:
5434:
5429:
5424:
5419:
5413:
5411:
5404:
5398:
5397:
5395:
5394:
5393:
5392:
5391:
5390:
5375:
5374:
5373:
5363:
5361:Classification
5358:
5353:
5348:
5343:
5338:
5333:
5327:
5325:
5319:
5318:
5316:
5315:
5310:
5308:McNemar's test
5305:
5300:
5295:
5290:
5284:
5282:
5272:
5271:
5254:
5247:
5246:
5243:
5242:
5239:
5238:
5236:
5235:
5230:
5225:
5220:
5214:
5212:
5206:
5205:
5203:
5202:
5186:
5180:
5178:
5172:
5171:
5169:
5168:
5163:
5158:
5153:
5148:
5146:Semiparametric
5143:
5138:
5132:
5130:
5126:
5125:
5123:
5122:
5117:
5112:
5107:
5101:
5099:
5093:
5092:
5090:
5089:
5084:
5079:
5074:
5069:
5063:
5061:
5055:
5054:
5052:
5051:
5046:
5041:
5036:
5030:
5028:
5018:
5017:
5014:
5013:
5008:
5002:
5001:
4994:
4993:
4990:
4989:
4986:
4985:
4983:
4982:
4981:
4980:
4970:
4965:
4960:
4959:
4958:
4953:
4942:
4940:
4934:
4933:
4930:
4929:
4927:
4926:
4921:
4920:
4919:
4911:
4903:
4887:
4884:(MannâWhitney)
4879:
4878:
4877:
4864:
4863:
4862:
4851:
4849:
4843:
4842:
4840:
4839:
4838:
4837:
4832:
4827:
4817:
4812:
4809:(ShapiroâWilk)
4804:
4799:
4794:
4789:
4784:
4776:
4770:
4768:
4762:
4761:
4759:
4758:
4750:
4741:
4729:
4723:
4721:Specific tests
4717:
4716:
4713:
4712:
4710:
4709:
4704:
4699:
4693:
4691:
4685:
4684:
4682:
4681:
4676:
4675:
4674:
4664:
4663:
4662:
4652:
4646:
4644:
4638:
4637:
4635:
4634:
4633:
4632:
4627:
4617:
4612:
4607:
4602:
4597:
4591:
4589:
4583:
4582:
4580:
4579:
4574:
4573:
4572:
4567:
4566:
4565:
4560:
4545:
4544:
4543:
4538:
4533:
4528:
4517:
4515:
4506:
4500:
4499:
4497:
4496:
4491:
4486:
4485:
4484:
4474:
4469:
4468:
4467:
4457:
4456:
4455:
4450:
4445:
4435:
4430:
4425:
4424:
4423:
4418:
4413:
4397:
4396:
4395:
4390:
4385:
4375:
4374:
4373:
4368:
4358:
4357:
4356:
4346:
4345:
4344:
4334:
4329:
4324:
4318:
4316:
4306:
4305:
4300:
4293:
4292:
4289:
4288:
4285:
4284:
4282:
4281:
4276:
4271:
4266:
4260:
4258:
4252:
4251:
4249:
4248:
4243:
4238:
4232:
4230:
4226:
4225:
4223:
4222:
4217:
4212:
4207:
4202:
4197:
4192:
4186:
4184:
4178:
4177:
4175:
4174:
4172:Standard error
4169:
4164:
4159:
4158:
4157:
4152:
4141:
4139:
4133:
4132:
4130:
4129:
4124:
4119:
4114:
4109:
4104:
4102:Optimal design
4099:
4094:
4088:
4086:
4076:
4075:
4070:
4063:
4062:
4059:
4058:
4055:
4054:
4052:
4051:
4046:
4041:
4036:
4031:
4026:
4021:
4016:
4011:
4006:
4001:
3996:
3991:
3986:
3981:
3975:
3973:
3967:
3966:
3964:
3963:
3958:
3957:
3956:
3951:
3941:
3936:
3930:
3928:
3922:
3921:
3919:
3918:
3913:
3908:
3902:
3900:
3899:Summary tables
3896:
3895:
3893:
3892:
3886:
3884:
3878:
3877:
3874:
3873:
3871:
3870:
3869:
3868:
3863:
3858:
3848:
3842:
3840:
3834:
3833:
3831:
3830:
3825:
3820:
3815:
3810:
3805:
3800:
3794:
3792:
3786:
3785:
3783:
3782:
3777:
3772:
3771:
3770:
3765:
3760:
3755:
3750:
3745:
3740:
3735:
3733:Contraharmonic
3730:
3725:
3714:
3712:
3703:
3693:
3692:
3687:
3680:
3679:
3677:
3676:
3671:
3665:
3662:
3661:
3656:
3654:
3653:
3646:
3639:
3631:
3622:
3621:
3619:
3618:
3613:
3608:
3596:
3591:
3585:
3582:
3581:
3579:
3578:
3573:
3568:
3560:
3559:
3554:
3543:
3538:
3533:
3528:
3522:
3514:
3513:
3508:
3503:
3498:
3490:
3489:
3484:
3479:
3474:
3466:
3464:
3451:
3450:
3448:
3447:
3442:
3436:
3435:
3423:
3411:
3406:
3398:
3397:
3389:
3384:
3376:
3375:
3370:
3365:
3359:
3357:
3346:
3345:
3343:
3342:
3337:
3332:
3325:
3320:
3315:
3310:
3305:
3300:
3292:
3290:
3279:
3278:
3276:
3275:
3270:
3265:
3260:
3255:
3250:
3243:Optimal design
3238:
3237:
3232:
3227:
3215:
3210:
3205:
3199:
3197:
3189:
3188:
3183:
3181:
3180:
3173:
3166:
3158:
3152:
3151:
3118:
3100:(4): 643â648.
3065:
3053:(4): 431â439.
3035:
2999:
2996:
2995:
2994:
2982:(2): 114â122.
2960:
2959:
2958:
2949:
2936:
2927:
2906:
2893:
2884:
2862:
2845:
2832:10.1.1.29.5355
2825:(3): 273â304.
2806:
2803:
2802:
2801:
2795:
2782:
2775:
2756:
2750:
2720:
2714:
2701:
2692:
2683:
2674:
2668:
2644:
2641:
2633:
2632:
2625:
2610:
2603:
2577:linear algebra
2568:
2565:
2564:
2563:
2557:
2540:
2534:
2511:
2508:
2506:
2503:
2501:
2498:
2497:
2496:
2490:
2477:
2471:
2449:
2421:(2): 174â196.
2406:
2400:
2383:
2377:
2349:
2338:
2329:
2320:
2314:
2298:
2292:
2268:
2265:
2263:
2262:
2230:
2228:
2227:
2216:
2206:Karlin, Samuel
2202:
2190:Shapley, Lloyd
2186:Karlin, Samuel
2162:
2154:discretization
2145:
2143:
2142:
2136:
2099:
2097:
2096:
2085:
2079:
2056:
2027:
2024:
2023:
2017:
1984:
1982:
1981:
1960:
1959:
1953:
1912:
1891:
1878:
1857:(2): 117â186.
1834:
1828:optimality", "
1817:
1800:
1791:
1788:
1787:
1771:on domains of
1726:
1706:
1697:
1688:
1680:
1662:
1643:
1634:
1624:
1607:
1604:
1603:
1589:
1559:
1520:
1485:
1443:
1418:
1401:
1392:
1353:
1308:
1295:
1293:, p. 176)
1282:
1280:
1277:
1275:
1274:
1269:
1264:
1259:
1254:
1249:
1244:
1239:
1234:
1229:
1224:
1219:
1214:
1209:
1204:
1199:
1194:
1189:
1183:
1181:
1178:
1166:Kirstine Smith
1126:
1123:
1081:
1078:
1061:
1058:
1056:
1053:
1043:, and optimal
1025:introduced by
972:
969:
946:Kirstine Smith
938:J. D. Gergonne
919:Main article:
916:
913:
878:Main article:
875:
872:
867:
864:
829:expected value
813:Main article:
810:
807:
805:and Atkinson.
779:
776:
774:
771:
767:global optimum
686:
683:
662:
652:
649:
613:
610:
601:
598:
574:
573:Implementation
571:
525:Main article:
522:
519:
518:
517:
516:
515:
498:
497:
496:
475:
474:
473:
444:
443:
442:
441:
432:
431:
430:
417:
416:
415:
394:
393:
392:
363:
362:
361:
348:
347:
346:
322:-optimality ("
289:inverse matrix
184:
181:
180:
179:
176:
173:
157:
154:
132:with the same
92:Kirstine Smith
46:Gustav Elfving
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
6015:
6004:
6001:
5999:
5996:
5994:
5991:
5989:
5986:
5984:
5981:
5979:
5976:
5974:
5971:
5969:
5966:
5964:
5961:
5960:
5958:
5943:
5942:
5933:
5931:
5930:
5921:
5919:
5918:
5913:
5907:
5905:
5904:
5895:
5894:
5891:
5877:
5874:
5872:
5871:Geostatistics
5869:
5867:
5864:
5862:
5859:
5857:
5854:
5853:
5851:
5849:
5845:
5839:
5838:Psychometrics
5836:
5834:
5831:
5829:
5826:
5824:
5821:
5819:
5816:
5814:
5811:
5809:
5806:
5804:
5801:
5799:
5796:
5794:
5791:
5790:
5788:
5786:
5782:
5776:
5773:
5771:
5768:
5766:
5762:
5759:
5757:
5754:
5752:
5749:
5747:
5744:
5743:
5741:
5739:
5735:
5729:
5726:
5724:
5721:
5719:
5715:
5712:
5710:
5707:
5706:
5704:
5702:
5701:Biostatistics
5698:
5694:
5690:
5685:
5681:
5663:
5662:Log-rank test
5660:
5659:
5657:
5653:
5647:
5644:
5643:
5641:
5639:
5635:
5629:
5626:
5624:
5621:
5619:
5616:
5614:
5611:
5610:
5608:
5606:
5602:
5599:
5597:
5593:
5583:
5580:
5578:
5575:
5573:
5570:
5568:
5565:
5563:
5560:
5559:
5557:
5555:
5551:
5545:
5542:
5540:
5537:
5535:
5533:(BoxâJenkins)
5529:
5527:
5524:
5522:
5519:
5515:
5512:
5511:
5510:
5507:
5506:
5504:
5502:
5498:
5492:
5489:
5487:
5486:DurbinâWatson
5484:
5482:
5476:
5474:
5471:
5469:
5468:DickeyâFuller
5466:
5465:
5463:
5459:
5453:
5450:
5448:
5445:
5443:
5442:Cointegration
5440:
5438:
5435:
5433:
5430:
5428:
5425:
5423:
5420:
5418:
5417:Decomposition
5415:
5414:
5412:
5408:
5405:
5403:
5399:
5389:
5386:
5385:
5384:
5381:
5380:
5379:
5376:
5372:
5369:
5368:
5367:
5364:
5362:
5359:
5357:
5354:
5352:
5349:
5347:
5344:
5342:
5339:
5337:
5334:
5332:
5329:
5328:
5326:
5324:
5320:
5314:
5311:
5309:
5306:
5304:
5301:
5299:
5296:
5294:
5291:
5289:
5288:Cohen's kappa
5286:
5285:
5283:
5281:
5277:
5273:
5269:
5265:
5261:
5257:
5252:
5248:
5234:
5231:
5229:
5226:
5224:
5221:
5219:
5216:
5215:
5213:
5211:
5207:
5201:
5197:
5193:
5187:
5185:
5182:
5181:
5179:
5177:
5173:
5167:
5164:
5162:
5159:
5157:
5154:
5152:
5149:
5147:
5144:
5142:
5141:Nonparametric
5139:
5137:
5134:
5133:
5131:
5127:
5121:
5118:
5116:
5113:
5111:
5108:
5106:
5103:
5102:
5100:
5098:
5094:
5088:
5085:
5083:
5080:
5078:
5075:
5073:
5070:
5068:
5065:
5064:
5062:
5060:
5056:
5050:
5047:
5045:
5042:
5040:
5037:
5035:
5032:
5031:
5029:
5027:
5023:
5019:
5012:
5009:
5007:
5004:
5003:
4999:
4995:
4979:
4976:
4975:
4974:
4971:
4969:
4966:
4964:
4961:
4957:
4954:
4952:
4949:
4948:
4947:
4944:
4943:
4941:
4939:
4935:
4925:
4922:
4918:
4912:
4910:
4904:
4902:
4896:
4895:
4894:
4891:
4890:Nonparametric
4888:
4886:
4880:
4876:
4873:
4872:
4871:
4865:
4861:
4860:Sample median
4858:
4857:
4856:
4853:
4852:
4850:
4848:
4844:
4836:
4833:
4831:
4828:
4826:
4823:
4822:
4821:
4818:
4816:
4813:
4811:
4805:
4803:
4800:
4798:
4795:
4793:
4790:
4788:
4785:
4783:
4781:
4777:
4775:
4772:
4771:
4769:
4767:
4763:
4757:
4755:
4751:
4749:
4747:
4742:
4740:
4735:
4731:
4730:
4727:
4724:
4722:
4718:
4708:
4705:
4703:
4700:
4698:
4695:
4694:
4692:
4690:
4686:
4680:
4677:
4673:
4670:
4669:
4668:
4665:
4661:
4658:
4657:
4656:
4653:
4651:
4648:
4647:
4645:
4643:
4639:
4631:
4628:
4626:
4623:
4622:
4621:
4618:
4616:
4613:
4611:
4608:
4606:
4603:
4601:
4598:
4596:
4593:
4592:
4590:
4588:
4584:
4578:
4575:
4571:
4568:
4564:
4561:
4559:
4556:
4555:
4554:
4551:
4550:
4549:
4546:
4542:
4539:
4537:
4534:
4532:
4529:
4527:
4524:
4523:
4522:
4519:
4518:
4516:
4514:
4510:
4507:
4505:
4501:
4495:
4492:
4490:
4487:
4483:
4480:
4479:
4478:
4475:
4473:
4470:
4466:
4465:loss function
4463:
4462:
4461:
4458:
4454:
4451:
4449:
4446:
4444:
4441:
4440:
4439:
4436:
4434:
4431:
4429:
4426:
4422:
4419:
4417:
4414:
4412:
4406:
4403:
4402:
4401:
4398:
4394:
4391:
4389:
4386:
4384:
4381:
4380:
4379:
4376:
4372:
4369:
4367:
4364:
4363:
4362:
4359:
4355:
4352:
4351:
4350:
4347:
4343:
4340:
4339:
4338:
4335:
4333:
4330:
4328:
4325:
4323:
4320:
4319:
4317:
4315:
4311:
4307:
4303:
4298:
4294:
4280:
4277:
4275:
4272:
4270:
4267:
4265:
4262:
4261:
4259:
4257:
4253:
4247:
4244:
4242:
4239:
4237:
4234:
4233:
4231:
4227:
4221:
4218:
4216:
4213:
4211:
4208:
4206:
4203:
4201:
4198:
4196:
4193:
4191:
4188:
4187:
4185:
4183:
4179:
4173:
4170:
4168:
4167:Questionnaire
4165:
4163:
4160:
4156:
4153:
4151:
4148:
4147:
4146:
4143:
4142:
4140:
4138:
4134:
4128:
4125:
4123:
4120:
4118:
4115:
4113:
4110:
4108:
4105:
4103:
4100:
4098:
4095:
4093:
4090:
4089:
4087:
4085:
4081:
4077:
4073:
4068:
4064:
4050:
4047:
4045:
4042:
4040:
4037:
4035:
4032:
4030:
4027:
4025:
4022:
4020:
4017:
4015:
4012:
4010:
4007:
4005:
4002:
4000:
3997:
3995:
3994:Control chart
3992:
3990:
3987:
3985:
3982:
3980:
3977:
3976:
3974:
3972:
3968:
3962:
3959:
3955:
3952:
3950:
3947:
3946:
3945:
3942:
3940:
3937:
3935:
3932:
3931:
3929:
3927:
3923:
3917:
3914:
3912:
3909:
3907:
3904:
3903:
3901:
3897:
3891:
3888:
3887:
3885:
3883:
3879:
3867:
3864:
3862:
3859:
3857:
3854:
3853:
3852:
3849:
3847:
3844:
3843:
3841:
3839:
3835:
3829:
3826:
3824:
3821:
3819:
3816:
3814:
3811:
3809:
3806:
3804:
3801:
3799:
3796:
3795:
3793:
3791:
3787:
3781:
3778:
3776:
3773:
3769:
3766:
3764:
3761:
3759:
3756:
3754:
3751:
3749:
3746:
3744:
3741:
3739:
3736:
3734:
3731:
3729:
3726:
3724:
3721:
3720:
3719:
3716:
3715:
3713:
3711:
3707:
3704:
3702:
3698:
3694:
3690:
3685:
3681:
3675:
3672:
3670:
3667:
3666:
3663:
3659:
3652:
3647:
3645:
3640:
3638:
3633:
3632:
3629:
3617:
3614:
3612:
3609:
3607:
3602:
3597:
3595:
3592:
3590:
3587:
3586:
3583:
3577:
3574:
3572:
3569:
3567:
3566:
3562:
3561:
3558:
3555:
3553:
3552:
3547:
3544:
3542:
3539:
3537:
3534:
3532:
3529:
3526:
3523:
3521:
3520:
3516:
3515:
3512:
3509:
3507:
3504:
3502:
3499:
3497:
3496:
3492:
3491:
3488:
3485:
3483:
3480:
3478:
3475:
3473:
3472:
3468:
3467:
3465:
3463:
3456:
3452:
3446:
3443:
3441:
3440:Compare means
3438:
3437:
3434:
3432:
3428:
3424:
3422:
3420:
3416:
3412:
3410:
3407:
3405:
3404:
3400:
3399:
3396:
3393:
3390:
3388:
3385:
3383:
3382:
3381:Random effect
3378:
3377:
3374:
3371:
3369:
3366:
3364:
3361:
3360:
3358:
3356:
3351:
3347:
3341:
3338:
3336:
3333:
3331:
3330:
3326:
3324:
3323:Orthogonality
3321:
3319:
3316:
3314:
3311:
3309:
3306:
3304:
3301:
3299:
3298:
3294:
3293:
3291:
3289:
3284:
3280:
3274:
3271:
3269:
3266:
3264:
3261:
3259:
3258:Randomization
3256:
3254:
3251:
3249:
3245:
3244:
3240:
3239:
3236:
3233:
3231:
3228:
3226:
3223:
3219:
3216:
3214:
3211:
3209:
3206:
3204:
3201:
3200:
3198:
3196:
3190:
3186:
3179:
3174:
3172:
3167:
3165:
3160:
3159:
3156:
3148:
3144:
3140:
3136:
3133:(1/2): 1â85.
3132:
3128:
3124:
3119:
3115:
3111:
3107:
3103:
3099:
3095:
3087:
3086:
3080:
3074:
3070:
3066:
3061:
3056:
3052:
3048:
3044:
3040:
3036:
3031:
3026:
3022:
3021:S. M. Stigler
3018:
3014:
3010:
3006:
3002:
3001:
2997:
2990:
2985:
2981:
2977:
2970:
2968:
2961:
2955:
2950:
2946:
2942:
2937:
2933:
2928:
2924:
2920:
2919:Admissibility
2916:
2912:
2907:
2903:
2899:
2894:
2890:
2885:
2881:
2877:
2874:
2869:
2868:
2865:
2859:
2855:
2851:
2846:
2842:
2838:
2833:
2828:
2824:
2820:
2819:
2814:
2809:
2808:
2804:
2798:
2792:
2788:
2783:
2778:
2772:
2768:
2764:
2763:
2757:
2753:
2747:
2743:
2739:
2738:
2733:
2732:Olkin, Ingram
2729:
2725:
2721:
2717:
2711:
2707:
2702:
2698:
2693:
2689:
2684:
2680:
2675:
2671:
2665:
2661:
2657:
2656:
2651:
2647:
2646:
2642:
2640:
2638:
2637:block designs
2628:
2622:
2618:
2617:
2611:
2606:
2600:
2596:
2595:
2590:
2589:Bailey, R. A.
2586:
2585:
2584:
2582:
2581:randomization
2578:
2574:
2573:block designs
2566:
2560:
2554:
2550:
2546:
2541:
2537:
2531:
2527:
2526:
2525:
2517:
2516:
2515:
2509:
2504:
2499:
2493:
2487:
2483:
2478:
2474:
2468:
2464:
2460:
2459:
2454:
2450:
2446:
2442:
2438:
2434:
2429:
2424:
2420:
2416:
2412:
2407:
2403:
2397:
2393:
2389:
2384:
2380:
2374:
2370:
2366:
2365:Sacks, Jerome
2362:
2361:Olkin, Ingram
2358:
2354:
2350:
2346:
2345:
2339:
2335:
2330:
2326:
2321:
2317:
2311:
2307:
2303:
2299:
2295:
2289:
2285:
2281:
2280:
2279:
2271:
2270:
2266:
2259:
2255:
2251:
2247:
2244:
2240:
2234:
2231:
2224:
2223:
2217:
2213:
2212:
2207:
2203:
2199:
2195:
2191:
2187:
2183:
2182:
2180:
2176:
2172:
2166:
2163:
2159:
2158:approximately
2155:
2149:
2146:
2139:
2133:
2129:
2128:
2123:
2119:
2118:
2116:
2112:
2109:
2103:
2100:
2093:
2092:
2086:
2082:
2076:
2072:
2071:
2065:
2064:
2060:
2057:
2053:
2049:
2045:
2041:
2037:
2031:
2028:
2020:
2014:
2010:
2005:
2004:
2002:
1998:
1994:
1988:
1985:
1978:
1974:
1970:
1966:
1965:
1963:
1956:
1950:
1946:
1942:
1941:
1936:
1932:
1928:
1927:
1925:
1921:
1920:Henry P. Wynn
1916:
1913:
1909:
1908:0-444-82061-2
1905:
1901:
1895:
1892:
1888:
1882:
1879:
1874:
1870:
1865:
1860:
1856:
1852:
1848:
1845:(June 1945).
1844:
1843:Wald, Abraham
1838:
1835:
1831:
1827:
1821:
1818:
1814:
1809:
1804:
1801:
1795:
1792:
1786:(book in pdf)
1783:
1782:
1777:
1776:
1774:
1770:
1766:
1762:
1758:
1755:
1751:
1747:
1744:
1740:
1736:
1730:
1727:
1723:
1720:
1716:
1710:
1707:
1701:
1698:
1692:
1689:
1683:
1677:
1673:
1666:
1663:
1659:
1658:
1654:
1647:
1644:
1638:
1635:
1628:
1625:
1621:
1617:
1611:
1608:
1602:(book in pdf)
1592:
1586:
1579:
1578:
1572:
1571:
1569:
1563:
1560:
1555:
1551:
1547:
1543:
1539:
1535:
1531:
1524:
1521:
1516:
1512:
1508:
1504:
1500:
1496:
1489:
1486:
1482:
1478:
1475:
1469:
1465:
1461:
1457:
1453:
1447:
1444:
1440:
1436:
1432:
1428:
1422:
1419:
1415:
1411:
1405:
1402:
1396:
1393:
1388:
1384:
1380:
1376:
1373:(1/2): 1â85.
1372:
1368:
1364:
1357:
1354:
1349:
1345:
1341:
1337:
1332:
1327:
1323:
1319:
1312:
1309:
1305:
1299:
1296:
1292:
1287:
1284:
1278:
1273:
1270:
1268:
1267:Wald, Abraham
1265:
1263:
1260:
1258:
1255:
1253:
1250:
1248:
1245:
1243:
1240:
1238:
1235:
1233:
1230:
1228:
1225:
1223:
1220:
1218:
1215:
1213:
1210:
1208:
1205:
1203:
1200:
1198:
1195:
1193:
1190:
1188:
1185:
1184:
1179:
1177:
1175:
1171:
1167:
1162:
1153:
1151:
1146:
1142:
1140:
1136:
1132:
1124:
1122:
1120:
1115:
1111:
1107:
1102:
1100:
1099:approximately
1096:
1091:
1087:
1079:
1077:
1075:
1071:
1067:
1059:
1054:
1052:
1050:
1046:
1042:
1038:
1034:
1032:
1028:
1024:
1020:
1016:
1012:
1008:
1004:
1000:
996:
992:
988:
982:
978:
970:
968:
966:
962:
958:
954:
949:
947:
943:
939:
934:
932:
928:
922:
914:
912:
910:
906:
902:
898:
894:
890:
886:
881:
873:
871:
865:
863:
860:
856:
853:The use of a
851:
849:
845:
841:
837:
834:
830:
826:
822:
816:
808:
806:
804:
800:
796:
792:
791:biostatistics
785:
777:
772:
770:
768:
764:
759:
757:
753:
750:
746:
742:
739:
735:
731:
728:
724:
720:
716:
712:
708:
704:
700:
696:
691:
684:
682:
680:
676:
672:
661:
656:
650:
648:
646:
642:
638:
634:
630:
626:
622:
620:
611:
609:
607:
599:
597:
595:
591:
587:
583:
578:
572:
570:
568:
564:
560:
556:
552:
548:
544:
540:
534:
528:
520:
513:
509:
508:
506:
503:-optimality (
502:
499:
494:
490:
486:
485:
483:
480:-optimality (
479:
476:
471:
467:
463:
459:
458:
456:
453:
452:
451:
449:
439:
438:
436:
433:
428:
424:
423:
421:
418:
413:
409:
405:
404:
402:
399:-optimality (
398:
395:
390:
386:
382:
378:
374:
373:
371:
368:-optimality (
367:
364:
359:
355:
354:
352:
349:
344:
340:
336:
332:
331:
329:
325:
321:
318:
317:
316:
314:
310:
306:
302:
298:
294:
290:
286:
282:
278:
274:
270:
266:
261:
259:
258:
254:
249:
248:
244:
239:
235:
231:
227:
224:
220:
216:
212:
208:
205:
201:
197:
193:
192:least squares
188:
182:
177:
174:
171:
167:
166:
165:
163:
155:
153:
151:
147:
142:
137:
135:
131:
127:
123:
119:
115:
111:
107:
104:
100:
95:
93:
89:
86:
82:
78:
74:
70:
66:
58:
54:
51:
47:
43:
37:
33:
19:
5939:
5927:
5908:
5901:
5813:Econometrics
5763: /
5746:Chemometrics
5723:Epidemiology
5716: /
5689:Applications
5531:ARIMA model
5478:Q-statistic
5427:Stationarity
5323:Multivariate
5266: /
5262: /
5260:Multivariate
5258: /
5198: /
5194: /
4968:Bayes factor
4867:Signed rank
4779:
4753:
4745:
4733:
4428:Completeness
4264:Cohort study
4162:Opinion poll
4097:Missing data
4084:Study design
4039:Scatter plot
3961:Scatter plot
3954:Spearman's Ď
3916:Grouped data
3563:
3549:
3531:Latin square
3517:
3493:
3469:
3430:
3426:
3419:multivariate
3418:
3414:
3401:
3379:
3327:
3295:
3241:
3130:
3126:
3097:
3093:
3084:
3072:
3069:Peirce, C. S
3050:
3046:
3016:
3012:
2979:
2975:
2966:
2953:
2944:
2931:
2922:
2901:
2888:
2879:
2853:
2822:
2816:
2786:
2761:
2736:
2705:
2696:
2687:
2678:
2654:
2634:
2615:
2593:
2570:
2548:
2523:
2521:
2513:
2481:
2457:
2418:
2414:
2391:
2368:
2343:
2333:
2324:
2305:
2277:
2275:
2257:
2253:
2249:
2243:Google Books
2242:
2238:
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2221:
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2197:
2193:
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2102:
2090:
2069:
2059:
2036:inefficiency
2030:
2008:
1997:inefficiency
1987:
1976:
1972:
1939:
1924:Abraham Wald
1915:
1899:
1894:
1886:
1881:
1854:
1850:
1837:
1829:
1825:
1820:
1803:
1794:
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1765:minimization
1729:
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1691:
1671:
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1651:
1646:
1637:
1627:
1610:
1594:. Retrieved
1576:
1562:
1540:(1): 57â70.
1537:
1533:
1523:
1498:
1494:
1488:
1479:, under the
1468:matrix trace
1446:
1421:
1404:
1395:
1370:
1366:
1356:
1321:
1317:
1311:
1303:
1298:
1286:
1247:Kiefer, Jack
1176:in London.)
1174:Karl Pearson
1164:
1155:
1143:
1128:
1103:
1083:
1073:
1065:
1063:
1048:
1039:are used in
1035:
1027:G. E. P. Box
1019:Armijo-style
1015:Boris Polyak
984:
950:
935:
924:
909:Abraham Wald
889:Abraham Wald
883:
869:
852:
818:
793:supporting
787:
760:
718:
706:
692:
688:
678:
674:
668:
658:
654:
636:
617:
615:
603:
579:
576:
536:
512:V-optimality
511:
504:
500:
492:
489:I-optimality
488:
481:
477:
462:G-optimality
461:
457:-optimality
454:
445:
437:-optimality
434:
422:-optimality
419:
408:E-optimality
407:
400:
396:
377:D-optimality
376:
369:
365:
353:-optimality
350:
335:A-optimality
334:
327:
323:
319:
267:has several
262:
256:
252:
251:
246:
242:
241:
189:
186:
159:
138:
109:
96:
72:
68:
62:
52:
5941:WikiProject
5856:Cartography
5818:Jurimetrics
5770:Reliability
5501:Time domain
5480:(LjungâBox)
5402:Time-series
5280:Categorical
5264:Time-series
5256:Categorical
5191:(Bernoulli)
5026:Correlation
5006:Correlation
4802:JarqueâBera
4774:Chi-squared
4536:M-estimator
4489:Asymptotics
4433:Sufficiency
4200:Interaction
4112:Replication
4092:Effect size
4049:Violin plot
4029:Radar chart
4009:Forest plot
3999:Correlogram
3949:Kendall's Ď
3506:BoxâBehnken
3387:Mixed model
3318:Confounding
3313:Interaction
3303:Effect size
3273:Sample size
2848:Ghosh, S.;
2545:Wynn, H. P.
2094:. Springer.
1596:October 15,
1464:determinant
1435:functionals
1431:information
1429:and other "
1097:to furnish
1095:discretized
891:. In 1972,
707:exactly one
690:criterion.
631:. On other
553:and in the
448:predictions
427:determinant
381:determinant
370:determinant
313:eigenvalues
309:functionals
305:information
257:information
234:"efficient"
217:theory for
85:statistical
5957:Categories
5808:Demography
5526:ARMA model
5331:Regression
4908:(Friedman)
4869:(Wilcoxon)
4807:Normality
4797:Lilliefors
4744:Student's
4620:Resampling
4494:Robustness
4482:divergence
4472:Efficiency
4410:(monotone)
4405:Likelihood
4322:Population
4155:Stratified
4107:Population
3926:Dependence
3882:Count data
3813:Percentile
3790:Dispersion
3723:Arithmetic
3658:Statistics
3462:randomized
3460:Completely
3431:covariance
3193:Scientific
3127:Biometrika
3075:: 197â201.
2998:Historical
2915:Invariance
2878:Designs".
2850:Rao, C. R.
2726:. (1985).
2267:References
1979:: 272â319.
1969:Kiefer, J.
1830:on-average
1632:Heiligers.
1534:Biometrika
1367:Biometrika
975:See also:
782:See also:
531:See also:
482:integrated
470:hat matrix
412:eigenvalue
401:eigenvalue
301:invariants
269:parameters
253:maximizing
243:minimizing
230:reciprocal
215:estimation
213:). In the
207:estimators
156:Advantages
130:parameters
103:estimating
53:(pictured)
5189:Logistic
4956:posterior
4882:Rank sum
4630:Jackknife
4625:Bootstrap
4443:Bootstrap
4378:Parameter
4327:Statistic
4122:Statistic
4034:Run chart
4019:Pie chart
4014:Histogram
4004:Fan chart
3979:Bar chart
3861:L-moments
3748:Geometric
3471:Factorial
3355:inference
3335:Covariate
3297:Treatment
3283:Treatment
2827:CiteSeerX
2011:. Wiley.
1757:conjugacy
1743:Wolfowitz
1737:to study
1719:Wolfowitz
1620:contrasts
1554:0006-3444
1474:partially
1348:121294724
1326:CiteSeerX
1090:supported
763:convexity
752:conjugacy
738:Wolfowitz
727:Wolfowitz
660:criteria.
641:benchmark
621:dependent
567:contrasts
559:contrasts
521:Contrasts
263:When the
226:parameter
221:with one
134:precision
116:and with
88:criterion
79:that are
57:Greenland
5903:Category
5596:Survival
5473:Johansen
5196:Binomial
5151:Isotonic
4738:(normal)
4383:location
4190:Blocking
4145:Sampling
4024:QâQ plot
3989:Box plot
3971:Graphics
3866:Skewness
3856:Kurtosis
3828:Variance
3758:Heronian
3753:Harmonic
3594:Category
3589:Glossary
3395:Bayesian
3373:Bayesian
3329:Blocking
3308:Contrast
3288:blocking
3248:Bayesian
3235:Blinding
3225:validity
3222:external
3218:Internal
2652:(1972).
2635:Optimal
2591:(2008).
2571:Optimal
2547:(1989).
2455:(2006).
2390:(1989).
2355:(1985).
2304:(1972).
2111:Archived
2048:blocking
1933:(1985).
1826:Bayesian
1750:Legendre
1618:and for
1180:See also
1088:that is
1074:a priori
1066:a priori
931:blocking
833:Bayesian
745:Legendre
663:â
565:and for
505:variance
466:diagonal
281:variance
279:and its
247:variance
204:unbiased
196:variance
126:estimate
5929:Commons
5876:Kriging
5761:Process
5718:studies
5577:Wavelet
5410:General
4577:Plug-in
4371:L space
4150:Cluster
3851:Moments
3669:Outline
3487:Taguchi
3455:Designs
3213:Control
3147:2331929
2445:1722074
2437:2676737
1999:of the
1873:2235829
1754:Fenchel
1503:Bibcode
1481:Loewner
1387:2331929
1139:Stigler
1125:History
1106:support
995:control
991:systems
989:and in
838:. Such
836:designs
749:Fenchel
717:). For
637:optimal
468:of the
383:of the
343:inverse
341:of the
324:average
311:of the
303:of the
97:In the
81:optimal
63:In the
5798:Census
5388:Normal
5336:Manova
5156:Robust
4906:2-way
4898:1-way
4736:-test
4407:
3984:Biplot
3775:Median
3768:Lehmer
3710:Center
3527:(GRBD)
3427:Ancova
3415:Manova
3350:Models
3195:method
3145:
3114:168276
3112:
2969:-cube"
2876:Robust
2860:
2829:
2793:
2773:
2748:
2712:
2666:
2623:
2601:
2555:
2532:
2488:
2469:
2443:
2435:
2398:
2375:
2312:
2290:
2246:Eprint
2175:Kiefer
2134:
2108:Polyak
2077:
2015:
1995:, the
1962:Kiefer
1951:
1906:
1871:
1739:Kiefer
1715:Kiefer
1678:
1657:robust
1587:
1552:
1385:
1346:
1328:
1324:: 64.
1110:Kiefer
1070:Sloane
821:models
734:Kiefer
723:Kiefer
719:convex
671:Kiefer
645:models
633:models
629:models
287:. The
285:matrix
277:vector
228:, the
5422:Trend
4951:prior
4893:anova
4782:-test
4756:-test
4748:-test
4655:Power
4600:Pivot
4393:shape
4388:scale
3838:Shape
3818:Range
3763:Heinz
3738:Cubic
3674:Index
3519:Block
3143:JSTOR
3110:JSTOR
2972:(PDF)
2873:Model
2433:JSTOR
2357:Brown
1869:JSTOR
1653:Model
1581:(PDF)
1383:JSTOR
1344:S2CID
1279:Notes
679:model
635:, an
625:model
619:model
594:model
584:like
339:trace
328:trace
326:" or
283:is a
5655:Test
4855:Sign
4707:Wald
3780:Mode
3718:Mean
3353:and
3286:and
3220:and
2858:ISBN
2791:ISBN
2771:ISBN
2746:ISBN
2710:ISBN
2664:ISBN
2660:SIAM
2621:ISBN
2599:ISBN
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2530:ISBN
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2152:The
2132:ISBN
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2034:The
2013:ISBN
1949:ISBN
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1763:The
1759:for
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1676:ISBN
1598:2011
1585:ISBN
1550:ISSN
1456:mean
1425:The
993:and
979:and
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754:for
588:and
273:mean
255:the
245:the
223:real
200:mean
128:the
101:for
71:(or
4835:BIC
4830:AIC
3135:doi
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3055:doi
3025:doi
2984:doi
2943:".
2900:".
2837:doi
2524:SAS
2423:doi
2278:SAS
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