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system, which is the one comprising the physical system, the feedback loop and the controller. This performance is typically achieved by designing the control law relying on a model of the system, which needs to be identified starting from experimental data. If the model identification procedure is
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A more common approach is therefore to start from measurements of the behavior of the system and the external influences (inputs to the system) and try to determine a mathematical relation between them without going into the details of what is actually happening inside the system. This approach is
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such models as well as model reduction. A common approach is to start from measurements of the behavior of the system and the external influences (inputs to the system) and try to determine a mathematical relation between them without going into many details of what is actually happening inside the
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A diagram describing the different methods for identifying systems. In the case of a "white box" we clearly see the structure of the system, and in a "black box" we know nothing about it except how it reacts to input. An intermediate state is a "gray box" state in which our knowledge of the system
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for control design depends not only on the plant/model mismatch but also on the controller that will be implemented. As such, in the I4C framework, given a control performance objective, the control engineer has to design the identification phase in such a way that the performance achieved by the
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methods. This approach is completely flexible and can be used with grey box models where the algorithms are primed with the known terms, or with completely black-box models where the model terms are selected as part of the identification procedure. Another advantage of this approach is that the
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Jin et al. describe grey-box modeling by assuming a model structure a priori and then estimating the model parameters. Parameter estimation is relatively easy if the model form is known but this is rarely the case. Alternatively, the structure or model terms for both linear and highly complex
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for microbial growth. The model contains a simple hyperbolic relationship between substrate concentration and growth rate, but this can be justified by molecules binding to a substrate without going into detail on the types of molecules or types of binding. Grey box modeling is also known as
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aimed at control purposes, what really matters is not to obtain the best possible model that fits the data, as in the classical system identification approach, but to obtain a model satisfying enough for the closed-loop performance. This more recent approach is called
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although the peculiarities of what is going on inside the system are not entirely known, a certain model based on both insight into the system and experimental data is constructed. This model does however still have a number of unknown free
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The reason why dedicated forward models are constructed is because it allows one to divide the overall control process. The first question is how to predict the future states of the system. That means, to simulate a
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can be realized. If it's unclear what the behavior of a system is, it's not possible to search for meaningful actions. The workflow for creating a forward model is called system identification. The idea is to
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The quality of system identification depends on the quality of the inputs, which are under the control of the systems engineer. Therefore, systems engineers have long used the principles of the
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algorithms will just select linear terms if the system under study is linear, and nonlinear terms if the system is nonlinear, which allows a great deal of flexibility in the identification.
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Sometimes, it is even more convenient to design a controller without explicitly identifying a model of the system, but directly working on experimental data. This is the case of
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1340:. For example, the robot starts in the maze and then the robot decides to move forward. Model predictive control determines the next action indirectly. The term
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266:, in which concepts of system identification are integrated into the controller design, and lay the foundations for formal controller optimality proofs.
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Nielsen, Henrik
Aalborg; Madsen, Henrik (January 2006). "Modelling the heat consumption in district heating systems using a grey-box approach".
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in a set of equations which will behave like the original system. The error between the real system and the forward model can be measured.
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is referencing to a forward model which doesn't provide the correct action but simulates a scenario. A forward model is equal to a
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Gevers, Michel (January 2005). "Identification for
Control: From the Early Achievements to the Revival of Experiment Design*".
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Spall, J. C. (2010), âFactorial Design for
Efficient Experimentation: Generating Informative Data for System Identification,â
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Gang Jin; Sain, M.K.; Pham, K.D.; Billie, F.S.; Ramallo, J.C. (2001). "Modeling MR-dampers: A nonlinear blackbox approach".
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Eric Wan and
Antonio Baptista and Magnus Carlsson and Richard Kiebutz and Yinglong Zhang and Alexander Bogdanov (2001).
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The idea behind I4C can be better understood by considering the following simple example. Consider a system with
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282:). Typically an input-output technique would be more accurate, but the input data is not always available.
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Kopicki, Marek and Zurek, Sebastian and
Stolkin, Rustam and Moerwald, Thomas and Wyatt, Jeremy L (2017).
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A dynamic mathematical model in this context is a mathematical description of the dynamic behavior of a
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called system identification. Two types of models are common in the field of system identification:
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Nonlinear System
Identification: NARMAX Methods in the Time, Frequency, and SpatioâTemporal Domains
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used in game programming. The model takes an input and calculates the future state of the system.
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1952:"Learning modular and transferable forward models of the motions of push manipulated objects"
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of input values which brings the plant into a goal state. This is called predictive control.
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1597:"Predicting the Heat Consumption in District Heating Systems using Meteorological Forecasts"
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Nguyen-Tuong, Duy and Peters, Jan (2011). "Model learning for robot control: a survey".
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may still be a model good enough for control purposes. In fact, if one wants to apply a
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Statistical methods to build mathematical models of dynamical systems from measured data
4262:
4257:
2720:
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2144:
Introduction to
Stochastic Search and Optimization: Estimation, Simulation, and Control
2036:, Van Nostrand Reinhold, New York, 1972 (2nd ed., Krieger Publ. Co., Malabar, FL, 1976)
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1250:. Thus, the two closed-loop transfer functions are indistinguishable. In conclusion,
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No prior model is available. Most system identification algorithms are of this type.
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1737:"Combining Semi-Physical and Neural Network Modeling: An Example of Its Usefulness"
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over a timespan for different input values. And the second task is to search for a
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1602:. Lyngby: Department of Mathematical Modelling, Technical University of Denmark.
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system if such feedback control law has to be applied. Whether or not a model is
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System identification techniques can utilize both input and output data (e.g.
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909:, the closed-loop transfer function from the reference to the output is, for
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1188:{\displaystyle {\frac {K{\hat {G}}(s)}{1+K{\hat {G}}(s)}}={\frac {K}{s+K}}.}
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which can be estimated using system identification. One example uses the
2118:, System Identification, Prentice Hall, Upper Saddle River, N.J., 1989.
2006:
1778:
Proceedings of the 2001 American
Control Conference. (Cat. No.01CH37148)
292:
Optimal design § System identification and stochastic approximation
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processes such as the movement of a falling body under the influence of
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One of the many possible applications of system identification is in
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or process in either the time or frequency domain. Examples include:
230:
300:. In recent decades, engineers have increasingly used the theory of
1999:
Model predictive neural control of a high-fidelity helicopter model
1042:{\displaystyle {\frac {KG_{0}(s)}{1+KG_{0}(s)}}={\frac {K}{s+1+K}}}
2080:
Stochastic
Approximation and Recursive Algorithms and Applications
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1557:
Dynamic System Identification: Experiment Design and Data Analysis
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System Identification and Model Reduction via Empirical Gramians
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There are many techniques available to create a forward model:
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A common understanding in Artificial Intelligence is that the
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2001:. {AIAA. American Institute of Aeronautics and Astronautics.
203:
from measured data. System identification also includes the
2166:
L. Ljung: Perspectives on System Identification, July 2008
2152:
Identification of Parametric Models from Experimental Data
1582:
Identification of Parametric Models from Experimental Data
1684:
Wimpenny, J.W.T. (April 1997). "The Validity of Models".
1595:
Nielsen, Henrik Aalborg; Madsen, Henrik (December 2000).
387:
applications, the objective of engineers is to obtain a
2041:
System Identification â Parameter and System Estimation
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Autoregressive conditional heteroskedasticity (ARCH)
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The forward model is the most important aspect of a
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From a classical system identification perspective,
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64:
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32:
2132:, 2nd Edition, IEEE Press, Wiley, New York, 2012.
2130:System Identification: A Frequency Domain Approach
2024:Goodwin, Graham C. & Payne, Robert L. (1977).
1555:Goodwin, Graham C. & Payne, Robert L. (1977).
1280:
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684:
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2071:, Prentice-Hall, Upper Saddle River, N.J., 1994.
210:for efficiently generating informative data for
3636:Multivariate adaptive regression splines (MARS)
327:, e.g. a model for a physical process from the
2191:
600:{\displaystyle {\hat {G}}(s)={\frac {1}{s}}.}
160:
8:
2092:: CS1 maint: multiple names: authors list (
1982:: CS1 maint: multiple names: authors list (
1935:: CS1 maint: multiple names: authors list (
278:) or can include only the output data (e.g.
2058:System Identification â Theory For the User
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2176:
2043:, John Wiley & Sons, New York, 1974.
262:. For example, it is the basis for modern
167:
153:
2150:Walter, Ăric & Pronzato, Luc (1997).
1967:
1752:
1580:Walter, Ăric & Pronzato, Luc (1997).
1387:like Box2d. A more recent technique is a
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502:{\displaystyle G_{0}(s)={\frac {1}{s+1}}}
481:
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424:
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370:nonlinear models can be identified using
1735:Forssell, U.; Lindskog, P. (July 1997).
1442:Nonlinear autoregressive exogenous model
1544:https://doi.org/10.1109/MCS.2010.937677
1494:
4162:KaplanâMeier estimator (product limit)
2085:
1975:
1928:
1631:
1620:
1383:is the classical one which is used in
766:at low frequency. What is more, while
29:
7:
4472:
4172:Accelerated failure time (AFT) model
1336:has to generate the next move for a
844:is a simply stable system. However,
4484:
3767:Analysis of variance (ANOVA, anova)
1432:Linear time-invariant system theory
3862:CochranâMantelâHaenszel statistics
2488:Pearson product-moment correlation
1817:Billings, Stephen A (2013-07-23).
1482:Black box model of power converter
1472:Grey box completion and validation
1367:. It has to be created before the
254:that react to external influences.
25:
2064:, Upper Saddle River, N.J., 1999.
276:eigensystem realization algorithm
183:System identification methods.png
4483:
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4459:
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1780:. IEEE. pp. 429-434 vol.1.
1391:for creating the forward model.
692:. In fact, modulus and phase of
215:system; this approach is called
40:
4121:Least-squares spectral analysis
2102:Nonlinear System Identification
1381:ordinary differential equations
1305:system is as high as possible.
367:nonlinear system identification
3102:Mean-unbiased minimum-variance
1301:model-based controller on the
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280:frequency domain decomposition
1:
4415:Geographic information system
3631:Simultaneous equations models
2069:Applied System Identification
1754:10.1016/s1474-6670(17)42938-7
1663:10.1016/j.enbuild.2005.05.002
1540:IEEE Control Systems Magazine
1281:{\displaystyle {\hat {G}}(s)}
1083:{\displaystyle {\hat {G}}(s)}
875:{\displaystyle {\hat {G}}(s)}
837:{\displaystyle {\hat {G}}(s)}
723:{\displaystyle {\hat {G}}(s)}
641:{\displaystyle {\hat {G}}(s)}
543:{\displaystyle {\hat {G}}(s)}
304:to specify inputs that yield
286:Optimal design of experiments
3598:Coefficient of determination
3209:Uniformly most powerful test
2082:(Second ed.). Springer.
1698:10.1177/08959374970110010601
1447:Open system (systems theory)
1243:{\displaystyle 1+K\approx K}
1218:is very large, one has that
730:are different from those of
4167:Proportional hazards models
4111:Spectral density estimation
4093:Vector autoregression (VAR)
3527:Maximum posterior estimator
2759:Randomized controlled trial
2128:R. Pintelon, J. Schoukens,
2078:and Yin, G. George (2003).
1852:European Journal of Control
1686:Advances in Dental Research
1510:. New York: Prentice Hall.
1322:data-driven control systems
302:optimal experimental design
270:Input-output vs output-only
264:data-driven control systems
4553:
3927:Multivariate distributions
2347:Average absolute deviation
1962:(5). Springer: 1061â1082.
1477:Data-driven control system
1417:Structural identifiability
889:controller with high gain
398:identification for control
379:Identification for control
289:
4441:
4244:
4231:
3915:Structural equation model
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3798:
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3251:Score/Lagrange multiplier
2857:
2844:
2666:Sample size determination
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2244:
2231:
2213:
2034:Identification of Systems
1969:10.1007/s10514-016-9571-3
1907:10.1007/s10339-011-0404-1
1542:, vol. 30(5), pp. 38â53.
1292:identified model for the
148:
122:
86:
69:
53:
39:
4512:Classical control theory
4410:Environmental statistics
3932:Elliptical distributions
3725:Generalized linear model
3654:Simple linear regression
3424:HodgesâLehmann estimator
2881:Probability distribution
2790:Stochastic approximation
2352:Coefficient of variation
1901:(4). Springer: 319â340.
1741:IFAC Proceedings Volumes
1313:structure is incomplete.
938:{\displaystyle G_{0}(s)}
795:{\displaystyle G_{0}(s)}
759:{\displaystyle G_{0}(s)}
685:{\displaystyle G_{0}(s)}
512:and an identified model
442:{\displaystyle G_{0}(s)}
4070:Cross-correlation (XCF)
3678:Non-standard predictors
3112:LehmannâScheffĂ© theorem
2785:Adaptive clinical trial
1786:10.1109/acc.2001.945582
352:semi-physical modeling.
221:system identification.
4522:Engineering statistics
4466:Mathematics portal
4287:Engineering statistics
4195:NelsonâAalen estimator
3772:Analysis of covariance
3659:Ordinary least squares
3583:Pearson product-moment
2987:Statistical functional
2898:Empirical distribution
2731:Controlled experiments
2460:Frequency distribution
2238:Descriptive statistics
1864:10.3166/ejc.11.335-352
1630:Cite journal requires
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349:Monod saturation model
184:
65:Methods and techniques
4382:Population statistics
4324:System identification
4058:Autocorrelation (ACF)
3986:Exponential smoothing
3900:Discriminant analysis
3895:Canonical correlation
3759:Partition of variance
3621:Regression validation
3465:(JonckheereâTerpstra)
3364:Likelihood-ratio test
3053:Frequentist inference
2965:Locationâscale family
2886:Sampling distribution
2851:Statistical inference
2818:Cross-sectional study
2805:Observational studies
2764:Randomized experiment
2593:Stem-and-leaf display
2395:Central limit theorem
2146:, Wiley, Hoboken, NJ.
2142:Spall, J. C. (2003),
1827:10.1002/9781118535561
1508:System identification
1502:Torsten, Söderström;
1467:Model order reduction
1407:Generalized filtering
1311:
1283:
1245:
1213:
1190:
1085:
1044:
940:
904:
877:
839:
804:asymptotically stable
797:
761:
725:
687:
643:
602:
545:
504:
444:
298:design of experiments
208:design of experiments
189:system identification
182:
143:Thermodynamic systems
112:System identification
18:System Identification
4305:Probabilistic design
3890:Principal components
3733:Exponential families
3685:Nonlinear regression
3664:General linear model
3626:Mixed effects models
3616:Errors and residuals
3593:Confounding variable
3495:Bayesian probability
3473:Van der Waerden test
3463:Ordered alternative
3228:Multiple comparisons
3107:RaoâBlackwellization
3070:Estimating equations
3026:Statistical distance
2744:Factorial experiment
2277:Arithmetic-Geometric
1895:Cognitive Processing
1651:Energy and Buildings
1427:Parameter estimation
1290:perfectly acceptable
1254:
1222:
1202:
1096:
1056:
951:
913:
893:
848:
810:
770:
734:
696:
660:
614:
557:
516:
456:
417:
315:White- and black-box
4527:Systems engineering
4377:Official statistics
4300:Methods engineering
3981:Seasonal adjustment
3749:Poisson regressions
3669:Bayesian regression
3608:Regression analysis
3588:Partial correlation
3560:Regression analysis
3159:Prediction interval
3154:Likelihood interval
3144:Confidence interval
3136:Interval estimation
3097:Unbiased estimators
2915:Model specification
2795:Up-and-down designs
2483:Partial correlation
2439:Index of dispersion
2357:Interquartile range
2007:10.2514/6.2001-4164
1452:Pattern recognition
884:purely proportional
197:mathematical models
193:statistical methods
139:Operations research
96:Pattern recognition
4397:Spatial statistics
4277:Medical statistics
4177:First hitting time
4131:Whittle likelihood
3782:Degrees of freedom
3777:Multivariate ANOVA
3710:Heteroscedasticity
3522:Bayesian estimator
3487:Bayesian inference
3336:KolmogorovâSmirnov
3221:Randomization test
3191:Testing hypotheses
3164:Tolerance interval
3075:Maximum likelihood
2970:Exponential family
2903:Density estimation
2863:Statistical theory
2823:Natural experiment
2769:Scientific control
2686:Survey methodology
2372:Standard deviation
2104:, Springer, 2001.
2076:Kushner, Harold J.
2039:Eykhoff, Pieter:
1559:. Academic Press.
1422:System realization
1374:formalize a system
1315:
1278:
1240:
1208:
1185:
1080:
1039:
935:
899:
872:
834:
792:
756:
720:
682:
638:
597:
540:
499:
439:
365:In the context of
319:One could build a
250:processes such as
185:
82:Related techniques
4537:Biological models
4517:Dynamical systems
4499:
4498:
4437:
4436:
4433:
4432:
4372:National accounts
4342:Actuarial science
4334:Social statistics
4227:
4226:
4223:
4222:
4219:
4218:
4154:Survival function
4139:
4138:
4001:Granger causality
3842:Contingency table
3817:Survival analysis
3794:
3793:
3790:
3789:
3646:Linear regression
3541:
3540:
3537:
3536:
3512:Credible interval
3481:
3480:
3264:
3263:
3080:Method of moments
2949:Parametric family
2910:Statistical model
2840:
2839:
2836:
2835:
2754:Random assignment
2676:Statistical power
2610:
2609:
2606:
2605:
2455:Contingency table
2425:
2424:
2292:Generalized/power
2138:978-0-470-64037-1
2028:. Academic Press.
1956:Autonomous Robots
1566:978-0-12-289750-4
1266:
1211:{\displaystyle K}
1180:
1159:
1146:
1114:
1068:
1037:
1010:
902:{\displaystyle K}
887:negative feedback
860:
822:
708:
626:
592:
569:
528:
497:
412:transfer function
306:maximally precise
201:dynamical systems
177:
176:
104:White-box testing
71:Black-box testing
34:Black box systems
16:(Redirected from
4544:
4487:
4486:
4475:
4474:
4464:
4463:
4449:
4448:
4352:Crime statistics
4246:
4233:
4150:
4116:Fourier analysis
4103:Frequency domain
4083:
4030:
3996:Structural break
3956:
3905:Cluster analysis
3852:Log-linear model
3825:
3800:
3741:
3715:Homoscedasticity
3571:
3547:
3466:
3458:
3450:
3449:(KruskalâWallis)
3434:
3419:
3374:Cross validation
3359:
3341:AndersonâDarling
3288:
3275:
3246:Likelihood-ratio
3238:Parametric tests
3216:Permutation test
3199:1- & 2-tails
3090:Minimum distance
3062:Point estimation
3058:
3009:Optimal decision
2960:
2859:
2846:
2828:Quasi-experiment
2778:Adaptive designs
2629:
2616:
2493:Rank correlation
2255:
2246:
2233:
2200:
2193:
2186:
2177:
2155:
2097:
2091:
2083:
2029:
2011:
2010:
1994:
1988:
1987:
1981:
1973:
1971:
1947:
1941:
1940:
1934:
1926:
1890:
1884:
1883:
1858:(4â5): 335â352.
1847:
1841:
1840:
1814:
1808:
1807:
1773:
1767:
1766:
1756:
1732:
1726:
1725:
1681:
1675:
1674:
1646:
1640:
1639:
1633:
1628:
1626:
1618:
1616:
1610:. Archived from
1601:
1592:
1586:
1585:
1577:
1571:
1570:
1552:
1546:
1536:
1530:
1529:
1499:
1287:
1285:
1284:
1279:
1268:
1267:
1259:
1249:
1247:
1246:
1241:
1217:
1215:
1214:
1209:
1194:
1192:
1191:
1186:
1181:
1179:
1165:
1160:
1158:
1148:
1147:
1139:
1126:
1116:
1115:
1107:
1100:
1089:
1087:
1086:
1081:
1070:
1069:
1061:
1048:
1046:
1045:
1040:
1038:
1036:
1016:
1011:
1009:
999:
998:
979:
969:
968:
955:
944:
942:
941:
936:
925:
924:
908:
906:
905:
900:
881:
879:
878:
873:
862:
861:
853:
843:
841:
840:
835:
824:
823:
815:
801:
799:
798:
793:
782:
781:
765:
763:
762:
757:
746:
745:
729:
727:
726:
721:
710:
709:
701:
691:
689:
688:
683:
672:
671:
652:, in general, a
647:
645:
644:
639:
628:
627:
619:
606:
604:
603:
598:
593:
585:
571:
570:
562:
549:
547:
546:
541:
530:
529:
521:
508:
506:
505:
500:
498:
496:
482:
468:
467:
448:
446:
445:
440:
429:
428:
389:good performance
329:Newton equations
325:first principles
169:
162:
155:
108:Gray-box testing
44:
30:
21:
4552:
4551:
4547:
4546:
4545:
4543:
4542:
4541:
4502:
4501:
4500:
4495:
4458:
4429:
4391:
4328:
4314:quality control
4281:
4263:Clinical trials
4240:
4215:
4199:
4187:Hazard function
4181:
4135:
4097:
4081:
4044:
4040:BreuschâGodfrey
4028:
4005:
3945:
3920:Factor analysis
3866:
3847:Graphical model
3819:
3786:
3753:
3739:
3719:
3673:
3640:
3602:
3565:
3564:
3533:
3477:
3464:
3456:
3448:
3432:
3417:
3396:Rank statistics
3390:
3369:Model selection
3357:
3315:Goodness of fit
3309:
3286:
3260:
3232:
3185:
3130:
3119:Median unbiased
3047:
2958:
2891:Order statistic
2853:
2832:
2799:
2773:
2725:
2680:
2623:
2621:Data collection
2602:
2514:
2469:
2443:
2421:
2381:
2333:
2250:Continuous data
2240:
2227:
2209:
2204:
2162:
2149:
2114:T. Söderström,
2100:Oliver Nelles:
2084:
2074:
2067:Jer-Nan Juang:
2032:Daniel Graupe:
2023:
2020:
2018:Further reading
2015:
2014:
1996:
1995:
1991:
1974:
1949:
1948:
1944:
1927:
1892:
1891:
1887:
1849:
1848:
1844:
1837:
1816:
1815:
1811:
1796:
1775:
1774:
1770:
1747:(11): 767â770.
1734:
1733:
1729:
1683:
1682:
1678:
1648:
1647:
1643:
1629:
1619:
1614:
1599:
1594:
1593:
1589:
1579:
1578:
1574:
1567:
1554:
1553:
1549:
1537:
1533:
1518:
1501:
1500:
1496:
1491:
1486:
1457:System dynamics
1437:Model selection
1397:
1385:physics engines
1330:
1252:
1251:
1220:
1219:
1200:
1199:
1169:
1127:
1101:
1094:
1093:
1054:
1053:
1020:
990:
980:
960:
956:
949:
948:
916:
911:
910:
891:
890:
846:
845:
808:
807:
773:
768:
767:
737:
732:
731:
694:
693:
663:
658:
657:
612:
611:
555:
554:
514:
513:
486:
459:
454:
453:
420:
415:
414:
385:control systems
381:
340:grey box model:
323:model based on
317:
294:
288:
272:
260:control systems
227:
173:
131:Control systems
77:
28:
23:
22:
15:
12:
11:
5:
4550:
4548:
4540:
4539:
4534:
4532:Systems theory
4529:
4524:
4519:
4514:
4504:
4503:
4497:
4496:
4494:
4493:
4481:
4469:
4455:
4442:
4439:
4438:
4435:
4434:
4431:
4430:
4428:
4427:
4422:
4417:
4412:
4407:
4401:
4399:
4393:
4392:
4390:
4389:
4384:
4379:
4374:
4369:
4364:
4359:
4354:
4349:
4344:
4338:
4336:
4330:
4329:
4327:
4326:
4321:
4316:
4307:
4302:
4297:
4291:
4289:
4283:
4282:
4280:
4279:
4274:
4269:
4260:
4258:Bioinformatics
4254:
4252:
4242:
4241:
4236:
4229:
4228:
4225:
4224:
4221:
4220:
4217:
4216:
4214:
4213:
4207:
4205:
4201:
4200:
4198:
4197:
4191:
4189:
4183:
4182:
4180:
4179:
4174:
4169:
4164:
4158:
4156:
4147:
4141:
4140:
4137:
4136:
4134:
4133:
4128:
4123:
4118:
4113:
4107:
4105:
4099:
4098:
4096:
4095:
4090:
4085:
4077:
4072:
4067:
4066:
4065:
4063:partial (PACF)
4054:
4052:
4046:
4045:
4043:
4042:
4037:
4032:
4024:
4019:
4013:
4011:
4010:Specific tests
4007:
4006:
4004:
4003:
3998:
3993:
3988:
3983:
3978:
3973:
3968:
3962:
3960:
3953:
3947:
3946:
3944:
3943:
3942:
3941:
3940:
3939:
3924:
3923:
3922:
3912:
3910:Classification
3907:
3902:
3897:
3892:
3887:
3882:
3876:
3874:
3868:
3867:
3865:
3864:
3859:
3857:McNemar's test
3854:
3849:
3844:
3839:
3833:
3831:
3821:
3820:
3803:
3796:
3795:
3792:
3791:
3788:
3787:
3785:
3784:
3779:
3774:
3769:
3763:
3761:
3755:
3754:
3752:
3751:
3735:
3729:
3727:
3721:
3720:
3718:
3717:
3712:
3707:
3702:
3697:
3695:Semiparametric
3692:
3687:
3681:
3679:
3675:
3674:
3672:
3671:
3666:
3661:
3656:
3650:
3648:
3642:
3641:
3639:
3638:
3633:
3628:
3623:
3618:
3612:
3610:
3604:
3603:
3601:
3600:
3595:
3590:
3585:
3579:
3577:
3567:
3566:
3563:
3562:
3557:
3551:
3550:
3543:
3542:
3539:
3538:
3535:
3534:
3532:
3531:
3530:
3529:
3519:
3514:
3509:
3508:
3507:
3502:
3491:
3489:
3483:
3482:
3479:
3478:
3476:
3475:
3470:
3469:
3468:
3460:
3452:
3436:
3433:(MannâWhitney)
3428:
3427:
3426:
3413:
3412:
3411:
3400:
3398:
3392:
3391:
3389:
3388:
3387:
3386:
3381:
3376:
3366:
3361:
3358:(ShapiroâWilk)
3353:
3348:
3343:
3338:
3333:
3325:
3319:
3317:
3311:
3310:
3308:
3307:
3299:
3290:
3278:
3272:
3270:Specific tests
3266:
3265:
3262:
3261:
3259:
3258:
3253:
3248:
3242:
3240:
3234:
3233:
3231:
3230:
3225:
3224:
3223:
3213:
3212:
3211:
3201:
3195:
3193:
3187:
3186:
3184:
3183:
3182:
3181:
3176:
3166:
3161:
3156:
3151:
3146:
3140:
3138:
3132:
3131:
3129:
3128:
3123:
3122:
3121:
3116:
3115:
3114:
3109:
3094:
3093:
3092:
3087:
3082:
3077:
3066:
3064:
3055:
3049:
3048:
3046:
3045:
3040:
3035:
3034:
3033:
3023:
3018:
3017:
3016:
3006:
3005:
3004:
2999:
2994:
2984:
2979:
2974:
2973:
2972:
2967:
2962:
2946:
2945:
2944:
2939:
2934:
2924:
2923:
2922:
2917:
2907:
2906:
2905:
2895:
2894:
2893:
2883:
2878:
2873:
2867:
2865:
2855:
2854:
2849:
2842:
2841:
2838:
2837:
2834:
2833:
2831:
2830:
2825:
2820:
2815:
2809:
2807:
2801:
2800:
2798:
2797:
2792:
2787:
2781:
2779:
2775:
2774:
2772:
2771:
2766:
2761:
2756:
2751:
2746:
2741:
2735:
2733:
2727:
2726:
2724:
2723:
2721:Standard error
2718:
2713:
2708:
2707:
2706:
2701:
2690:
2688:
2682:
2681:
2679:
2678:
2673:
2668:
2663:
2658:
2653:
2651:Optimal design
2648:
2643:
2637:
2635:
2625:
2624:
2619:
2612:
2611:
2608:
2607:
2604:
2603:
2601:
2600:
2595:
2590:
2585:
2580:
2575:
2570:
2565:
2560:
2555:
2550:
2545:
2540:
2535:
2530:
2524:
2522:
2516:
2515:
2513:
2512:
2507:
2506:
2505:
2500:
2490:
2485:
2479:
2477:
2471:
2470:
2468:
2467:
2462:
2457:
2451:
2449:
2448:Summary tables
2445:
2444:
2442:
2441:
2435:
2433:
2427:
2426:
2423:
2422:
2420:
2419:
2418:
2417:
2412:
2407:
2397:
2391:
2389:
2383:
2382:
2380:
2379:
2374:
2369:
2364:
2359:
2354:
2349:
2343:
2341:
2335:
2334:
2332:
2331:
2326:
2321:
2320:
2319:
2314:
2309:
2304:
2299:
2294:
2289:
2284:
2282:Contraharmonic
2279:
2274:
2263:
2261:
2252:
2242:
2241:
2236:
2229:
2228:
2226:
2225:
2220:
2214:
2211:
2210:
2205:
2203:
2202:
2195:
2188:
2180:
2174:
2173:
2168:
2161:
2160:External links
2158:
2157:
2156:
2147:
2140:
2126:
2112:
2098:
2072:
2065:
2060:, 2nd ed, PTR
2051:
2037:
2030:
2019:
2016:
2013:
2012:
1989:
1942:
1885:
1842:
1835:
1809:
1795:978-0780364950
1794:
1768:
1727:
1692:(1): 150â159.
1676:
1641:
1632:|journal=
1617:on 2017-04-21.
1587:
1572:
1565:
1547:
1531:
1517:978-0138812362
1516:
1493:
1492:
1490:
1487:
1485:
1484:
1479:
1474:
1469:
1464:
1462:Systems theory
1459:
1454:
1449:
1444:
1439:
1434:
1429:
1424:
1419:
1414:
1409:
1404:
1398:
1396:
1393:
1389:neural network
1365:MPC-controller
1346:physics engine
1329:
1326:
1277:
1274:
1271:
1265:
1262:
1239:
1236:
1233:
1230:
1227:
1207:
1196:
1195:
1184:
1178:
1175:
1172:
1168:
1163:
1157:
1154:
1151:
1145:
1142:
1136:
1133:
1130:
1125:
1122:
1119:
1113:
1110:
1104:
1079:
1076:
1073:
1067:
1064:
1050:
1049:
1035:
1032:
1029:
1026:
1023:
1019:
1014:
1008:
1005:
1002:
997:
993:
989:
986:
983:
978:
975:
972:
967:
963:
959:
934:
931:
928:
923:
919:
898:
871:
868:
865:
859:
856:
833:
830:
827:
821:
818:
791:
788:
785:
780:
776:
755:
752:
749:
744:
740:
719:
716:
713:
707:
704:
681:
678:
675:
670:
666:
637:
634:
631:
625:
622:
608:
607:
596:
591:
588:
583:
580:
577:
574:
568:
565:
539:
536:
533:
527:
524:
510:
509:
495:
492:
489:
485:
480:
477:
474:
471:
466:
462:
438:
435:
432:
427:
423:
380:
377:
363:
362:
353:
316:
313:
290:Main article:
287:
284:
271:
268:
256:
255:
245:
226:
223:
175:
174:
172:
171:
164:
157:
149:
146:
145:
120:
119:
115:
114:
84:
83:
79:
78:
67:
66:
62:
61:
59:Oracle machine
51:
50:
46:
45:
37:
36:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
4549:
4538:
4535:
4533:
4530:
4528:
4525:
4523:
4520:
4518:
4515:
4513:
4510:
4509:
4507:
4492:
4491:
4482:
4480:
4479:
4470:
4468:
4467:
4462:
4456:
4454:
4453:
4444:
4443:
4440:
4426:
4423:
4421:
4420:Geostatistics
4418:
4416:
4413:
4411:
4408:
4406:
4403:
4402:
4400:
4398:
4394:
4388:
4387:Psychometrics
4385:
4383:
4380:
4378:
4375:
4373:
4370:
4368:
4365:
4363:
4360:
4358:
4355:
4353:
4350:
4348:
4345:
4343:
4340:
4339:
4337:
4335:
4331:
4325:
4322:
4320:
4317:
4315:
4311:
4308:
4306:
4303:
4301:
4298:
4296:
4293:
4292:
4290:
4288:
4284:
4278:
4275:
4273:
4270:
4268:
4264:
4261:
4259:
4256:
4255:
4253:
4251:
4250:Biostatistics
4247:
4243:
4239:
4234:
4230:
4212:
4211:Log-rank test
4209:
4208:
4206:
4202:
4196:
4193:
4192:
4190:
4188:
4184:
4178:
4175:
4173:
4170:
4168:
4165:
4163:
4160:
4159:
4157:
4155:
4151:
4148:
4146:
4142:
4132:
4129:
4127:
4124:
4122:
4119:
4117:
4114:
4112:
4109:
4108:
4106:
4104:
4100:
4094:
4091:
4089:
4086:
4084:
4082:(BoxâJenkins)
4078:
4076:
4073:
4071:
4068:
4064:
4061:
4060:
4059:
4056:
4055:
4053:
4051:
4047:
4041:
4038:
4036:
4035:DurbinâWatson
4033:
4031:
4025:
4023:
4020:
4018:
4017:DickeyâFuller
4015:
4014:
4012:
4008:
4002:
3999:
3997:
3994:
3992:
3991:Cointegration
3989:
3987:
3984:
3982:
3979:
3977:
3974:
3972:
3969:
3967:
3966:Decomposition
3964:
3963:
3961:
3957:
3954:
3952:
3948:
3938:
3935:
3934:
3933:
3930:
3929:
3928:
3925:
3921:
3918:
3917:
3916:
3913:
3911:
3908:
3906:
3903:
3901:
3898:
3896:
3893:
3891:
3888:
3886:
3883:
3881:
3878:
3877:
3875:
3873:
3869:
3863:
3860:
3858:
3855:
3853:
3850:
3848:
3845:
3843:
3840:
3838:
3837:Cohen's kappa
3835:
3834:
3832:
3830:
3826:
3822:
3818:
3814:
3810:
3806:
3801:
3797:
3783:
3780:
3778:
3775:
3773:
3770:
3768:
3765:
3764:
3762:
3760:
3756:
3750:
3746:
3742:
3736:
3734:
3731:
3730:
3728:
3726:
3722:
3716:
3713:
3711:
3708:
3706:
3703:
3701:
3698:
3696:
3693:
3691:
3690:Nonparametric
3688:
3686:
3683:
3682:
3680:
3676:
3670:
3667:
3665:
3662:
3660:
3657:
3655:
3652:
3651:
3649:
3647:
3643:
3637:
3634:
3632:
3629:
3627:
3624:
3622:
3619:
3617:
3614:
3613:
3611:
3609:
3605:
3599:
3596:
3594:
3591:
3589:
3586:
3584:
3581:
3580:
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3576:
3572:
3568:
3561:
3558:
3556:
3553:
3552:
3548:
3544:
3528:
3525:
3524:
3523:
3520:
3518:
3515:
3513:
3510:
3506:
3503:
3501:
3498:
3497:
3496:
3493:
3492:
3490:
3488:
3484:
3474:
3471:
3467:
3461:
3459:
3453:
3451:
3445:
3444:
3443:
3440:
3439:Nonparametric
3437:
3435:
3429:
3425:
3422:
3421:
3420:
3414:
3410:
3409:Sample median
3407:
3406:
3405:
3402:
3401:
3399:
3397:
3393:
3385:
3382:
3380:
3377:
3375:
3372:
3371:
3370:
3367:
3365:
3362:
3360:
3354:
3352:
3349:
3347:
3344:
3342:
3339:
3337:
3334:
3332:
3330:
3326:
3324:
3321:
3320:
3318:
3316:
3312:
3306:
3304:
3300:
3298:
3296:
3291:
3289:
3284:
3280:
3279:
3276:
3273:
3271:
3267:
3257:
3254:
3252:
3249:
3247:
3244:
3243:
3241:
3239:
3235:
3229:
3226:
3222:
3219:
3218:
3217:
3214:
3210:
3207:
3206:
3205:
3202:
3200:
3197:
3196:
3194:
3192:
3188:
3180:
3177:
3175:
3172:
3171:
3170:
3167:
3165:
3162:
3160:
3157:
3155:
3152:
3150:
3147:
3145:
3142:
3141:
3139:
3137:
3133:
3127:
3124:
3120:
3117:
3113:
3110:
3108:
3105:
3104:
3103:
3100:
3099:
3098:
3095:
3091:
3088:
3086:
3083:
3081:
3078:
3076:
3073:
3072:
3071:
3068:
3067:
3065:
3063:
3059:
3056:
3054:
3050:
3044:
3041:
3039:
3036:
3032:
3029:
3028:
3027:
3024:
3022:
3019:
3015:
3014:loss function
3012:
3011:
3010:
3007:
3003:
3000:
2998:
2995:
2993:
2990:
2989:
2988:
2985:
2983:
2980:
2978:
2975:
2971:
2968:
2966:
2963:
2961:
2955:
2952:
2951:
2950:
2947:
2943:
2940:
2938:
2935:
2933:
2930:
2929:
2928:
2925:
2921:
2918:
2916:
2913:
2912:
2911:
2908:
2904:
2901:
2900:
2899:
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2892:
2889:
2888:
2887:
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2882:
2879:
2877:
2874:
2872:
2869:
2868:
2866:
2864:
2860:
2856:
2852:
2847:
2843:
2829:
2826:
2824:
2821:
2819:
2816:
2814:
2811:
2810:
2808:
2806:
2802:
2796:
2793:
2791:
2788:
2786:
2783:
2782:
2780:
2776:
2770:
2767:
2765:
2762:
2760:
2757:
2755:
2752:
2750:
2747:
2745:
2742:
2740:
2737:
2736:
2734:
2732:
2728:
2722:
2719:
2717:
2716:Questionnaire
2714:
2712:
2709:
2705:
2702:
2700:
2697:
2696:
2695:
2692:
2691:
2689:
2687:
2683:
2677:
2674:
2672:
2669:
2667:
2664:
2662:
2659:
2657:
2654:
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2649:
2647:
2644:
2642:
2639:
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2636:
2634:
2630:
2626:
2622:
2617:
2613:
2599:
2596:
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2584:
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2579:
2576:
2574:
2571:
2569:
2566:
2564:
2561:
2559:
2556:
2554:
2551:
2549:
2546:
2544:
2543:Control chart
2541:
2539:
2536:
2534:
2531:
2529:
2526:
2525:
2523:
2521:
2517:
2511:
2508:
2504:
2501:
2499:
2496:
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2327:
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2256:
2253:
2251:
2247:
2243:
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2234:
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2224:
2221:
2219:
2216:
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2212:
2208:
2201:
2196:
2194:
2189:
2187:
2182:
2181:
2178:
2172:
2169:
2167:
2164:
2163:
2159:
2153:
2148:
2145:
2141:
2139:
2135:
2131:
2127:
2125:
2124:0-13-881236-5
2121:
2117:
2113:
2111:
2110:3-540-67369-5
2107:
2103:
2099:
2095:
2089:
2081:
2077:
2073:
2070:
2066:
2063:
2062:Prentice Hall
2059:
2055:
2054:Lennart Ljung
2052:
2050:
2049:0-471-24980-7
2046:
2042:
2038:
2035:
2031:
2027:
2022:
2021:
2017:
2008:
2004:
2000:
1993:
1990:
1985:
1979:
1970:
1965:
1961:
1957:
1953:
1946:
1943:
1938:
1932:
1924:
1920:
1916:
1912:
1908:
1904:
1900:
1896:
1889:
1886:
1881:
1877:
1873:
1869:
1865:
1861:
1857:
1853:
1846:
1843:
1838:
1836:9781118535561
1832:
1828:
1824:
1820:
1813:
1810:
1805:
1801:
1797:
1791:
1787:
1783:
1779:
1772:
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1755:
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1746:
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1523:
1519:
1513:
1509:
1505:
1498:
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1488:
1483:
1480:
1478:
1475:
1473:
1470:
1468:
1465:
1463:
1460:
1458:
1455:
1453:
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1435:
1433:
1430:
1428:
1425:
1423:
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1415:
1413:
1410:
1408:
1405:
1403:
1400:
1399:
1394:
1392:
1390:
1386:
1382:
1377:
1375:
1370:
1366:
1361:
1359:
1355:
1349:
1347:
1343:
1339:
1335:
1328:Forward model
1327:
1325:
1323:
1320:
1310:
1306:
1304:
1299:
1295:
1291:
1272:
1260:
1237:
1234:
1231:
1228:
1225:
1205:
1182:
1176:
1173:
1170:
1166:
1161:
1152:
1140:
1134:
1131:
1128:
1120:
1108:
1102:
1092:
1091:
1090:
1074:
1062:
1033:
1030:
1027:
1024:
1021:
1017:
1012:
1003:
995:
991:
987:
984:
981:
973:
965:
961:
957:
947:
946:
945:
929:
921:
917:
896:
888:
885:
866:
854:
828:
816:
805:
786:
778:
774:
750:
742:
738:
714:
702:
676:
668:
664:
655:
651:
632:
620:
594:
589:
586:
581:
575:
563:
553:
552:
551:
534:
522:
493:
490:
487:
483:
478:
472:
464:
460:
452:
451:
450:
433:
425:
421:
413:
410:
405:
403:
399:
394:
390:
386:
378:
376:
373:
368:
360:
358:
354:
350:
346:
341:
338:
337:
336:
332:
330:
326:
322:
314:
312:
310:
307:
303:
299:
293:
285:
283:
281:
277:
269:
267:
265:
261:
253:
252:stock markets
249:
246:
243:
239:
236:
235:
234:
232:
224:
222:
220:
219:
213:
209:
206:
202:
198:
194:
190:
187:The field of
181:
170:
165:
163:
158:
156:
151:
150:
147:
144:
140:
136:
132:
128:
126:
121:
116:
113:
109:
105:
101:
97:
93:
89:
85:
80:
76:
72:
68:
63:
60:
56:
52:
47:
43:
38:
35:
31:
19:
4488:
4476:
4457:
4450:
4362:Econometrics
4323:
4312: /
4295:Chemometrics
4272:Epidemiology
4265: /
4238:Applications
4080:ARIMA model
4027:Q-statistic
3976:Stationarity
3872:Multivariate
3815: /
3811: /
3809:Multivariate
3807: /
3747: /
3743: /
3517:Bayes factor
3416:Signed rank
3328:
3302:
3294:
3282:
2977:Completeness
2813:Cohort study
2711:Opinion poll
2646:Missing data
2633:Study design
2588:Scatter plot
2510:Scatter plot
2503:Spearman's Ï
2465:Grouped data
2151:
2143:
2129:
2101:
2079:
2068:
2057:
2040:
2033:
2025:
1998:
1992:
1978:cite journal
1959:
1955:
1945:
1931:cite journal
1898:
1894:
1888:
1855:
1851:
1845:
1818:
1812:
1777:
1771:
1744:
1740:
1730:
1689:
1685:
1679:
1657:(1): 63â71.
1654:
1650:
1644:
1623:cite journal
1612:the original
1590:
1581:
1575:
1556:
1550:
1539:
1534:
1507:
1497:
1378:
1362:
1350:
1331:
1318:
1316:
1302:
1297:
1293:
1289:
1197:
1051:
653:
649:
609:
511:
408:
406:
401:
397:
382:
364:
355:
339:
333:
318:
295:
273:
257:
228:
216:
188:
186:
135:Open systems
124:
118:Fundamentals
111:
88:Feed forward
4490:WikiProject
4405:Cartography
4367:Jurimetrics
4319:Reliability
4050:Time domain
4029:(LjungâBox)
3951:Time-series
3829:Categorical
3813:Time-series
3805:Categorical
3740:(Bernoulli)
3575:Correlation
3555:Correlation
3351:JarqueâBera
3323:Chi-squared
3085:M-estimator
3038:Asymptotics
2982:Sufficiency
2749:Interaction
2661:Replication
2641:Effect size
2598:Violin plot
2578:Radar chart
2558:Forest plot
2548:Correlogram
2498:Kendall's Ï
2154:. Springer.
1584:. Springer.
1298:appropriate
393:closed-loop
127:information
92:Obfuscation
75:Blackboxing
4506:Categories
4357:Demography
4075:ARMA model
3880:Regression
3457:(Friedman)
3418:(Wilcoxon)
3356:Normality
3346:Lilliefors
3293:Student's
3169:Resampling
3043:Robustness
3031:divergence
3021:Efficiency
2959:(monotone)
2954:Likelihood
2871:Population
2704:Stratified
2656:Population
2475:Dependence
2431:Count data
2362:Percentile
2339:Dispersion
2272:Arithmetic
2207:Statistics
1504:Stoica, P.
1489:References
1412:Hysteresis
1334:controller
656:model for
404:in short.
345:parameters
309:estimators
3738:Logistic
3505:posterior
3431:Rank sum
3179:Jackknife
3174:Bootstrap
2992:Bootstrap
2927:Parameter
2876:Statistic
2671:Statistic
2583:Run chart
2568:Pie chart
2563:Histogram
2553:Fan chart
2528:Bar chart
2410:L-moments
2297:Geometric
2116:P. Stoica
2088:cite book
1872:0947-3580
1763:1474-6670
1706:0895-9374
1671:0378-7788
1608:134091581
1402:Black box
1264:^
1235:≈
1144:^
1112:^
1066:^
858:^
820:^
706:^
624:^
567:^
526:^
357:black box
321:white-box
218:black box
195:to build
100:White box
55:Black box
4452:Category
4145:Survival
4022:Johansen
3745:Binomial
3700:Isotonic
3287:(normal)
2932:location
2739:Blocking
2694:Sampling
2573:QâQ plot
2538:Box plot
2520:Graphics
2415:Skewness
2405:Kurtosis
2377:Variance
2307:Heronian
2302:Harmonic
1915:21487784
1880:13054338
1804:62730770
1722:23008333
1526:16983523
1506:(1989).
1395:See also
1358:sequence
1052:and for
806:system,
248:economic
238:physical
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4310:Process
4267:studies
4126:Wavelet
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