2267:
the plane, but a person who arrives after can not, a discontinuity and asymmetry which makes arriving slightly late much more costly than arriving slightly early. In drug dosing, the cost of too little drug may be lack of efficacy, while the cost of too much may be tolerable toxicity, another example of asymmetry. Traffic, pipes, beams, ecologies, climates, etc. may tolerate increased load or stress with little noticeable change up to a point, then become backed up or break catastrophically. These situations, Deming and Taleb argue, are common in real-life problems, perhaps more common than classical smooth, continuous, symmetric, differentials cases.
374:
1194:- it minimises the average loss over all possible states of nature θ, over all possible (probability-weighted) data outcomes. One advantage of the Bayesian approach is to that one need only choose the optimal action under the actual observed data to obtain a uniformly optimal one, whereas choosing the actual frequentist optimal decision rule as a function of all possible observations, is a much more difficult problem. Of equal importance though, the Bayes Rule reflects consideration of loss outcomes under different states of nature, θ.
5269:
168:
1157:
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6189:
898:
33:
5293:
1952:
5281:
796:
1152:{\displaystyle \rho (\pi ^{*},a)=\int _{\Theta }\int _{\mathbf {X}}L(\theta ,a({\mathbf {x}}))\,\mathrm {d} P({\mathbf {x}}\vert \theta )\,\mathrm {d} \pi ^{*}(\theta )=\int _{\mathbf {X}}\int _{\Theta }L(\theta ,a({\mathbf {x}}))\,\mathrm {d} \pi ^{*}(\theta \vert {\mathbf {x}})\,\mathrm {d} M({\mathbf {x}})}
1778:
2266:
argue that empirical reality, not nice mathematical properties, should be the sole basis for selecting loss functions, and real losses often are not mathematically nice and are not differentiable, continuous, symmetric, etc. For example, a person who arrives before a plane gate closure can still make
1962:
Sound statistical practice requires selecting an estimator consistent with the actual acceptable variation experienced in the context of a particular applied problem. Thus, in the applied use of loss functions, selecting which statistical method to use to model an applied problem depends on knowing
553:
data that were elicited through computer-assisted interviews with decision makers. Among other things, he constructed objective functions to optimally distribute budgets for 16 Westfalian universities and the
European subsidies for equalizing unemployment rates among 271 German regions.
2251:
The choice of a loss function is not arbitrary. It is very restrictive and sometimes the loss function may be characterized by its desirable properties. Among the choice principles are, for example, the requirement of completeness of the class of symmetric statistics in the case of
531:
In many applications, objective functions, including loss functions as a particular case, are determined by the problem formulation. In other situations, the decision makerâs preference must be elicited and represented by a scalar-valued function (called also
1759:
2417:
Constructing Scalar-Valued
Objective Functions. Proceedings of the Third International Conference on Econometric Decision Models: Constructing Scalar-Valued Objective Functions, University of Hagen, held in Katholische Akademie Schwerte September 5â8,
216:, i.e., the loss associated with a decision should be the difference between the consequences of the best decision that could have been made had the underlying circumstances been known and the decision that was in fact taken before they were known.
1421:
639:
2451:
Constructing and
Applying Objective Functions. Proceedings of the Fourth International Conference on Econometric Decision Models Constructing and Applying Objective Functions, University of Hagen, held in Haus Nordhelle, August, 28 â 31,
1947:{\displaystyle {\underset {\delta }{\operatorname {arg\,min} }}\operatorname {E} _{\theta \in \Theta }={\underset {\delta }{\operatorname {arg\,min} }}\ \int _{\theta \in \Theta }R(\theta ,\delta )\,p(\theta )\,d\theta .}
1323:
1637:
1651:
of the uncertain variable of interest, such as end-of-period wealth. Since the value of this variable is uncertain, so is the value of the utility function; it is the expected value of utility that is maximized.
544:
showed that the most usable objective functions â quadratic and additive â are determined by a few indifference points. He used this property in the models for constructing these objective functions from either
1546:
1676:
6083:
1332:
1982:
is the estimator that minimizes expected loss experienced under the absolute-difference loss function. Still different estimators would be optimal under other, less common circumstances.
838:
299:
540:
has highlighted in his Nobel Prize lecture. The existing methods for constructing objective functions are collected in the proceedings of two dedicated conferences. In particular,
473:
366:, the expected value of the quadratic form is used. The quadratic loss assigns more importance to outliers than to the true data due to its square nature, so alternatives like the
2238:
1234:
515:
5925:
791:{\displaystyle R(\theta ,\delta )=\operatorname {E} _{\theta }L{\big (}\theta ,\delta (X){\big )}=\int _{X}L{\big (}\theta ,\delta (x){\big )}\,\mathrm {d} P_{\theta }(x).}
5331:
2082:
2131:
350:. In these problems, even in the absence of uncertainty, it may not be possible to achieve the desired values of all target variables. Often loss is expressed as a
4390:
2157:
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1648:
1554:
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176:
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1464:
124:, and the event in question is some function of the difference between estimated and true values for an instance of data. The concept, as old as
1989:, the objective function is simply expressed as the expected value of a monetary quantity, such as profit, income, or end-of-period wealth. For
236:, as well as being symmetric: an error above the target causes the same loss as the same magnitude of error below the target. If the target is
5324:
2885:
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2467:
2433:
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3005:
6215:
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308:; the value of the constant makes no difference to a decision, and can be ignored by setting it equal to 1. This is also known as the
6027:
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In some contexts, the value of the loss function itself is a random quantity because it depends on the outcome of a random variable
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600:
We first define the expected loss in the frequentist context. It is obtained by taking the expected value with respect to the
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3998:
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2622:
2483:
Tangian, Andranik (2002). "Constructing a quasi-concave quadratic objective function from interviewing a decision maker".
1549:
117:, etc.), in which case it is to be maximized. The loss function could include terms from several levels of the hierarchy.
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4773:
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1170:(θ | x) is the posterior distribution, and the order of integration has been changed. One then should choose the action
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145:
86:
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1673:: Choose the decision rule with the lowest worst loss â that is, minimize the worst-case (maximum possible) loss:
816:
6220:
6078:
5717:
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5371:
4734:
4502:
4223:
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4006:
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3765:
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3194:
1754:{\displaystyle {\underset {\delta }{\operatorname {arg\,min} }}\ \max _{\theta \in \Theta }\ R(\theta ,\delta ).}
161:
70:
4847:
6119:
5376:
5217:
4984:
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866:
601:
212:
198:
141:
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2782:
Detailed information on mathematical principles of the loss function choice is given in
Chapter 2 of the book
246:
232:
techniques. It is often more mathematically tractable than other loss functions because of the properties of
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3592:
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2032:
4887:
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1974:
or average is the statistic for estimating location that minimizes the expected loss experienced under the
403:
152:, it is used in an insurance context to model benefits paid over premiums, particularly since the works of
6124:
5884:
5603:
5598:
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4466:
3463:
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3146:
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2024:
1432:
810:
355:
5285:
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2186:
6154:
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6104:
5792:
5692:
5560:
5189:
5131:
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4702:
4428:
4312:
4171:
4053:
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3734:
3693:
3658:
3625:
3571:
3546:
3501:
3440:
3400:
3202:
3025:
2955:
Waud, Roger N. (1976). "Asymmetric
Policymaker Utility Functions and Optimal Policy under Uncertainty".
2263:
359:
332:
6022:
5268:
4158:
2581:
1416:{\displaystyle R(\theta ,{\hat {\theta }})=\operatorname {E} _{\theta }(\theta -{\hat {\theta }})^{2}.}
1210:
485:
6174:
6129:
5575:
5520:
5366:
5361:
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125:
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94:
41:
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3290:
3246:
3164:
3089:
2991:
2028:
1963:
the losses that will be experienced from being wrong under the problem's particular circumstances.
1764:
854:
328:
172:
6188:
4834:
2391:
Frisch, Ragnar (1969). "From utopian theory to practical applications: the case of econometrics".
6134:
5712:
5541:
5273:
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4938:
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3739:
3710:
3670:
3630:
3576:
3493:
3179:
3174:
2972:
2553:
Tangian, Andranik (2004). "Redistribution of university budgets with respect to the status quo".
2535:
2500:
2329:
2085:
2039:
2017:
1967:
1447:
1439:
1428:
1326:
1241:
882:
363:
225:
2045:
2830:
167:
6200:
5992:
5644:
5515:
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4664:
4649:
4624:
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3933:
3850:
3794:
3717:
3561:
3483:
3262:
3136:
2881:
2853:
2805:
2763:
2730:
2689:
2681:
2653:
2582:"Multi-criteria optimization of regional employment policy: A simulation analysis for Germany"
2463:
2429:
2339:
2325:
2259:
2091:
340:
203:
149:
51:
2857:
2518:
Tangian, Andranik (2004). "A model for ordinally constructing additive objective functions".
592:
of the loss function; however, this quantity is defined differently under the two paradigms.
5945:
5935:
5742:
5536:
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5481:
5424:
5412:
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5159:
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4910:
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4712:
4644:
4522:
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3635:
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2918:
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2593:
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2527:
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2455:
2421:
2301:
550:
541:
153:
114:
110:
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2744:
2703:
2667:
354:
in the deviations of the variables of interest from their desired values; this approach is
6058:
6002:
5824:
5466:
5386:
5121:
4865:
4727:
4654:
4329:
4203:
4176:
4153:
4122:
3749:
3744:
3698:
3428:
3079:
2891:
2740:
2699:
2663:
2276:
546:
479:
391:
157:
106:
102:
74:
2136:
2877:
2649:
2454:. Lecture Notes in Economics and Mathematical Systems. Vol. 510. Berlin: Springer.
2420:. Lecture Notes in Economics and Mathematical Systems. Vol. 453. Berlin: Springer.
6032:
5997:
5987:
5812:
5570:
5396:
5070:
5065:
3528:
3458:
3104:
2166:
2005:
1772:
1451:
589:
351:
2566:
2531:
2496:
6237:
5977:
5957:
5874:
5553:
5227:
5194:
5057:
5018:
4829:
4798:
4262:
4216:
3523:
3350:
3114:
3109:
2945:
2849:
2597:
2159:. The squared loss has the disadvantage that it has the tendency to be dominated by
2013:
1990:
1975:
1661:
537:
336:
229:
137:
3380:
2539:
2504:
6063:
5894:
5169:
5102:
5079:
4994:
4324:
3620:
3518:
3453:
3395:
3317:
3272:
2906:
2296:
2133:. However the absolute loss has the disadvantage that it is not differentiable at
1986:
526:
129:
101:
is either a loss function or its opposite (in specific domains, variously called a
46:
2333:
17:
2639:
6159:
5930:
5839:
5834:
5456:
5434:
5212:
5174:
4857:
4758:
4620:
4433:
4400:
3892:
3809:
3804:
3448:
3405:
3385:
3365:
3355:
3124:
2360:
1994:
581:
90:
2001:, and the objective function to be optimized is the expected value of utility.
1664:
makes a choice using an optimality criterion. Some commonly used criteria are:
6053:
6012:
6007:
5920:
5829:
5737:
5649:
5629:
4058:
3538:
3238:
3169:
3119:
3094:
3014:
2459:
2425:
2291:
387:
367:
180:
6048:
6017:
5915:
5759:
5722:
5659:
5613:
5608:
5593:
4211:
4063:
3683:
3478:
3390:
3375:
3370:
3335:
2922:
2009:
1647:
In economics, decision-making under uncertainty is often modelled using the
1424:
320:
133:
5309:
1318:{\displaystyle L(\theta ,{\hat {\theta }})=(\theta -{\hat {\theta }})^{2},}
370:, Log-Cosh and SMAE losses are used when the data has many large outliers.
2726:
5950:
5782:
3727:
3345:
3222:
3217:
3212:
3184:
2831:"Asymmetric Loss Functions and the Rationality of Expected Stock Returns"
1771:
Choose the decision rule with the lowest average loss (i.e. minimize the
1632:{\displaystyle R(f,{\hat {f}})=\operatorname {E} \|f-{\hat {f}}\|^{2}.\,}
233:
6073:
5910:
5864:
5787:
5687:
5682:
5634:
5232:
4933:
2976:
2160:
1998:
1669:
1455:
533:
207:
2256:
observations, the principle of complete information, and some others.
148:, it is the penalty for an incorrect classification of an example. In
6088:
6068:
5940:
5732:
5154:
4135:
4109:
4089:
3340:
3131:
2253:
1979:
1768:: Choose the decision rule which satisfies an invariance requirement.
377:
Effect of using different loss functions, when the data has outliers.
324:
160:, the loss is the penalty for failing to achieve a desired value. In
85:(sometimes also called an error function) is a function that maps an
2968:
2829:
Aretz, Kevin; Bartram, SĂśhnke M.; Pope, Peter F. (AprilâJune 2011).
2240:), the final sum tends to be the result of a few particularly large
1178:. In the latter equation, the integrand inside dx is known as the
2721:. Springer Texts in Statistics (2nd ed.). New York: Springer.
93:
intuitively representing some "cost" associated with the event. An
5889:
5869:
5859:
5854:
5849:
5844:
5807:
5639:
536:
function) in a form suitable for optimization â the problem that
372:
166:
5879:
3074:
1971:
881:
In a
Bayesian approach, the expectation is calculated using the
5313:
5043:
4610:
4357:
3656:
3426:
3043:
2987:
2784:
Klebanov, B.; Rachev, Svetlozat T.; Fabozzi, Frank J. (2009).
1186:
also minimizes the overall Bayes Risk. This optimal decision,
26:
2983:
2932:
Horowitz, Ann R. (1987). "Loss functions and public policy".
66:
Mathematical relation assigning a probability event to a cost
1174:
which minimises this expected loss, which is referred to as
2027:, it is desirable to have a loss function that is globally
1541:{\displaystyle L(f,{\hat {f}})=\|f-{\hat {f}}\|_{2}^{2}\,,}
588:
statistical theory involve making a decision based on the
809:
is a vector of observations stochastically drawn from a
343:
theory, which is based on the quadratic loss function.
2189:
1446:
itself. The loss function is typically chosen to be a
132:
in the middle of the 20th century. In the context of
120:
In statistics, typically a loss function is used for
2169:
2139:
2094:
2048:
1781:
1679:
1557:
1467:
1335:
1250:
1213:
901:
819:
642:
488:
406:
249:
4896:
Autoregressive conditional heteroskedasticity (ARCH)
6097:
6041:
5970:
5903:
5775:
5675:
5668:
5622:
5586:
5529:
5405:
5345:
5203:
5140:
5093:
5056:
5011:
4993:
4960:
4951:
4909:
4856:
4817:
4766:
4757:
4678:
4635:
4565:
4531:
4485:
4452:
4414:
4381:
4293:
4202:
4121:
4076:
4044:
3997:
3942:
3868:
3859:
3669:
3611:
3585:
3537:
3492:
3439:
3326:
3281:
3255:
3237:
3193:
3145:
3065:
3056:
629:. Here the decision rule depends on the outcome of
210:, the loss function should be based on the idea of
2244:-values, rather than an expression of the average
2232:
2175:
2151:
2125:
2076:
1946:
1753:
1631:
1540:
1415:
1317:
1228:
1151:
832:
790:
509:
467:
293:
2870:Statistical decision theory and Bayesian Analysis
2641:Statistical decision theory and Bayesian Analysis
2004:Other measures of cost are possible, for example
840:is the expectation over all population values of
805:is a fixed but possibly unknown state of nature,
1712:
865:) and the integral is evaluated over the entire
228:loss function is common, for example when using
4444:Multivariate adaptive regression splines (MARS)
206:argued that using non-Bayesian methods such as
2907:"Making monetary policy: Objectives and rules"
2038:Two very commonly used loss functions are the
1997:agents, loss is measured as the negative of a
1970:". Under typical statistical assumptions, the
5325:
2999:
1182:, and minimising it with respect to decision
755:
730:
707:
682:
164:, the function is mapped to a monetary loss.
8:
2788:. New York: Nova Scientific Publishers, Inc.
1616:
1594:
1520:
1498:
1114:
1002:
833:{\displaystyle \operatorname {E} _{\theta }}
346:The quadratic loss function is also used in
2872:(2nd ed.). New York: Springer-Verlag.
2644:(2nd ed.). New York: Springer-Verlag.
40:It has been suggested that this article be
5672:
5332:
5318:
5310:
5053:
5040:
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4632:
4607:
4378:
4354:
4082:
3865:
3666:
3653:
3436:
3423:
3062:
3053:
3040:
3006:
2992:
2984:
2786:Robust and Non-Robust Models in Statistics
290:
89:or values of one or more variables onto a
2449:Tangian, Andranik; Gruber, Josef (2002).
2415:Tangian, Andranik; Gruber, Josef (1997).
2319:
2317:
2221:
2205:
2194:
2188:
2168:
2138:
2118:
2110:
2093:
2068:
2047:
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1921:
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1404:
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770:
761:
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729:
728:
719:
706:
705:
681:
680:
668:
641:
521:Constructing loss and objective functions
490:
489:
487:
443:
442:
414:
413:
405:
394:, a frequently used loss function is the
348:linear-quadratic optimal control problems
284:
248:
183:, and Log-Cosh Loss) used for regression
2586:Review of Urban and Regional Development
2555:European Journal of Operational Research
2520:European Journal of Operational Research
2485:European Journal of Operational Research
1649:von NeumannâMorgenstern utility function
294:{\displaystyle \lambda (x)=C(t-x)^{2}\;}
2313:
4970:KaplanâMeier estimator (product limit)
1966:A common example involves estimating "
482:notation, i.e. it evaluates to 1 when
97:seeks to minimize a loss function. An
1166:wherein θ has been "integrated out,"
468:{\displaystyle L({\hat {y}},y)=\left}
171:Comparison of common loss functions (
7:
6170:Generative adversarial network (GAN)
5280:
4980:Accelerated failure time (AFT) model
2838:International Journal of Forecasting
2335:The Elements of Statistical Learning
2233:{\textstyle \sum _{i=1}^{n}L(a_{i})}
240:, then a quadratic loss function is
128:, was reintroduced in statistics by
5292:
4575:Analysis of variance (ANOVA, anova)
1207:, a decision function whose output
4670:CochranâMantelâHaenszel statistics
3296:Pearson product-moment correlation
2378:On the mathematical theory of risk
1898:
1875:
1872:
1869:
1865:
1862:
1859:
1821:
1811:
1801:
1798:
1795:
1791:
1788:
1785:
1722:
1699:
1696:
1693:
1689:
1686:
1683:
1588:
1367:
1129:
1094:
1056:
1013:
985:
935:
821:
762:
665:
617:. This is also referred to as the
25:
2613:"Risk of a statistical procedure"
2282:Loss functions for classification
1643:Economic choice under uncertainty
1240:, and a quadratic loss function (
633:. The risk function is given by:
6208:
6207:
6187:
5291:
5279:
5267:
5254:
5253:
2911:Oxford Review of Economic Policy
2850:10.1016/j.ijforecast.2009.10.008
2598:10.1111/j.1467-940X.2008.00144.x
1229:{\displaystyle {\hat {\theta }}}
1141:
1119:
1081:
1045:
997:
972:
946:
510:{\displaystyle {\hat {y}}\neq y}
31:
4929:Least-squares spectral analysis
1985:In economics, when an agent is
136:, for example, this is usually
6120:Recurrent neural network (RNN)
6110:Differentiable neural computer
3910:Mean-unbiased minimum-variance
2362:Statistical Decision Functions
2227:
2214:
2119:
2111:
2104:
2098:
2058:
2052:
1931:
1925:
1918:
1906:
1850:
1847:
1835:
1829:
1745:
1733:
1609:
1582:
1576:
1561:
1548:the risk function becomes the
1513:
1492:
1486:
1471:
1401:
1394:
1379:
1360:
1354:
1339:
1325:the risk function becomes the
1303:
1296:
1281:
1275:
1269:
1254:
1220:
1146:
1136:
1124:
1108:
1089:
1086:
1076:
1064:
1033:
1027:
1008:
992:
980:
977:
967:
955:
924:
905:
782:
776:
750:
744:
702:
696:
658:
646:
495:
448:
431:
419:
410:
281:
268:
259:
253:
1:
6165:Variational autoencoder (VAE)
6125:Long short-term memory (LSTM)
5392:Computational learning theory
5223:Geographic information system
4439:Simultaneous equations models
2762:. Berlin: Walter de Gruyter.
2760:Parametric Statistical Theory
2717:Robert, Christian P. (2007).
2686:Optimal Statistical Decisions
2567:10.1016/S0377-2217(03)00271-6
2532:10.1016/S0377-2217(03)00413-2
2497:10.1016/S0377-2217(01)00185-0
2394:The Nobel PrizeâPrize Lecture
1550:mean integrated squared error
358:because it results in linear
6145:Convolutional neural network
4406:Coefficient of determination
4017:Uniformly most powerful test
2946:10.1016/0164-0704(87)90016-4
2163:âwhen summing over a set of
6140:Multilayer perceptron (MLP)
4975:Proportional hazards models
4919:Spectral density estimation
4901:Vector autoregression (VAR)
4335:Maximum posterior estimator
3567:Randomized controlled trial
2800:Deming, W. Edwards (2000).
2618:Encyclopedia of Mathematics
1442:, the unknown parameter is
1162:where m(x) is known as the
564:Empirical risk minimization
6265:
6216:Artificial neural networks
6130:Gated recurrent unit (GRU)
5356:Differentiable programming
4735:Multivariate distributions
3155:Average absolute deviation
2688:. Wiley Classics Library.
2580:Tangian, Andranik (2008).
2077:{\displaystyle L(a)=a^{2}}
561:
524:
196:
6183:
5549:Artificial neural network
5372:Automatic differentiation
5249:
5052:
5039:
4723:Structural equation model
4631:
4606:
4377:
4353:
4085:
4059:Score/Lagrange multiplier
3665:
3652:
3474:Sample size determination
3435:
3422:
3052:
3039:
3021:
2934:Journal of Macroeconomics
2460:10.1007/978-3-642-56038-5
2426:10.1007/978-3-642-48773-6
1978:loss function, while the
1958:Selecting a loss function
596:Frequentist expected loss
162:financial risk management
71:mathematical optimization
57:Proposed since July 2024.
5377:Neuromorphic engineering
5340:Differentiable computing
5218:Environmental statistics
4740:Elliptical distributions
4533:Generalized linear model
4462:Simple linear regression
4232:HodgesâLehmann estimator
3689:Probability distribution
3598:Stochastic approximation
3160:Coefficient of variation
2338:. Springer. p. 18.
2126:{\displaystyle L(a)=|a|}
1427:found by minimizing the
857:over the event space of
613:, of the observed data,
602:probability distribution
199:Regret (decision theory)
6150:Residual neural network
5566:Artificial Intelligence
4878:Cross-correlation (XCF)
4486:Non-standard predictors
3920:LehmannâScheffĂŠ theorem
3593:Adaptive clinical trial
2790:(and references there).
2611:Nikulin, M.S. (2001) ,
2287:Discounted maximum loss
2025:optimization algorithms
1775:of the loss function):
1236:is an estimate of
1203:For a scalar parameter
220:Quadratic loss function
5274:Mathematics portal
5095:Engineering statistics
5003:NelsonâAalen estimator
4580:Analysis of covariance
4467:Ordinary least squares
4391:Pearson product-moment
3795:Statistical functional
3706:Empirical distribution
3539:Controlled experiments
3268:Frequency distribution
3046:Descriptive statistics
2905:Cecchetti, S. (2000).
2234:
2210:
2177:
2153:
2127:
2078:
1948:
1755:
1633:
1542:
1433:Posterior distribution
1417:
1319:
1230:
1198:Examples in statistics
1153:
888:of the parameter
861:(parametrized by
834:
792:
511:
469:
378:
360:first-order conditions
339:methods applied using
295:
184:
6105:Neural Turing machine
5693:Human image synthesis
5190:Population statistics
5132:System identification
4866:Autocorrelation (ACF)
4794:Exponential smoothing
4708:Discriminant analysis
4703:Canonical correlation
4567:Partition of variance
4429:Regression validation
4273:(JonckheereâTerpstra)
4172:Likelihood-ratio test
3861:Frequentist inference
3773:Locationâscale family
3694:Sampling distribution
3659:Statistical inference
3626:Cross-sectional study
3613:Observational studies
3572:Randomized experiment
3401:Stem-and-leaf display
3203:Central limit theorem
2923:10.1093/oxrep/16.4.43
2758:Pfanzagl, J. (1994).
2727:10.1007/0-387-71599-1
2264:Nassim Nicholas Taleb
2235:
2190:
2178:
2154:
2128:
2079:
1949:
1756:
1634:
1543:
1418:
1320:
1231:
1192:Bayes (decision) Rule
1164:predictive likelihood
1154:
835:
793:
621:of the decision rule
512:
470:
376:
335:, and much else, use
333:design of experiments
296:
170:
6196:Computer programming
6175:Graph neural network
5750:Text-to-video models
5728:Text-to-image models
5576:Large language model
5561:Scientific computing
5367:Statistical manifold
5362:Information geometry
5113:Probabilistic design
4698:Principal components
4541:Exponential families
4493:Nonlinear regression
4472:General linear model
4434:Mixed effects models
4424:Errors and residuals
4401:Confounding variable
4303:Bayesian probability
4281:Van der Waerden test
4271:Ordered alternative
4036:Multiple comparisons
3915:RaoâBlackwellization
3878:Estimating equations
3834:Statistical distance
3552:Factorial experiment
3085:Arithmetic-Geometric
2380:. Centraltryckeriet.
2187:
2167:
2137:
2092:
2046:
1779:
1677:
1555:
1465:
1333:
1248:
1211:
899:
817:
640:
486:
404:
362:. In the context of
247:
122:parameter estimation
95:optimization problem
5542:In-context learning
5382:Pattern recognition
5185:Official statistics
5108:Methods engineering
4789:Seasonal adjustment
4557:Poisson regressions
4477:Bayesian regression
4416:Regression analysis
4396:Partial correlation
4368:Regression analysis
3967:Prediction interval
3962:Likelihood interval
3952:Confidence interval
3944:Interval estimation
3905:Unbiased estimators
3723:Model specification
3603:Up-and-down designs
3291:Partial correlation
3247:Index of dispersion
3165:Interquartile range
2878:1985sdtb.book.....B
2719:The Bayesian Choice
2650:1985sdtb.book.....B
2376:CramĂŠr, H. (1930).
2330:Friedman, Jerome H.
2152:{\displaystyle a=0}
1533:
1454:. For example, for
1444:probability density
855:probability measure
517:, and 0 otherwise.
6135:Echo state network
6023:JĂźrgen Schmidhuber
5718:Facial recognition
5713:Speech recognition
5623:Software libraries
5205:Spatial statistics
5085:Medical statistics
4985:First hitting time
4939:Whittle likelihood
4590:Degrees of freedom
4585:Multivariate ANOVA
4518:Heteroscedasticity
4330:Bayesian estimator
4295:Bayesian inference
4144:KolmogorovâSmirnov
4029:Randomization test
3999:Testing hypotheses
3972:Tolerance interval
3883:Maximum likelihood
3778:Exponential family
3711:Density estimation
3671:Statistical theory
3631:Natural experiment
3577:Scientific control
3494:Survey methodology
3180:Standard deviation
2326:Tibshirani, Robert
2230:
2173:
2149:
2123:
2074:
2018:safety engineering
1944:
1882:
1808:
1751:
1726:
1706:
1629:
1538:
1519:
1450:in an appropriate
1440:density estimation
1429:Mean squared error
1413:
1327:mean squared error
1315:
1242:squared error loss
1226:
1149:
883:prior distribution
830:
788:
625:and the parameter
507:
465:
379:
364:stochastic control
310:squared error loss
304:for some constant
291:
185:
99:objective function
18:Squared error loss
6244:Optimal decisions
6231:
6230:
5993:Stephen Grossberg
5966:
5965:
5307:
5306:
5245:
5244:
5241:
5240:
5180:National accounts
5150:Actuarial science
5142:Social statistics
5035:
5034:
5031:
5030:
5027:
5026:
4962:Survival function
4947:
4946:
4809:Granger causality
4650:Contingency table
4625:Survival analysis
4602:
4601:
4598:
4597:
4454:Linear regression
4349:
4348:
4345:
4344:
4320:Credible interval
4289:
4288:
4072:
4071:
3888:Method of moments
3757:Parametric family
3718:Statistical model
3648:
3647:
3644:
3643:
3562:Random assignment
3484:Statistical power
3418:
3417:
3414:
3413:
3263:Contingency table
3233:
3232:
3100:Generalized/power
2887:978-0-387-96098-2
2804:. The MIT Press.
2802:Out of the Crisis
2769:978-3-11-013863-4
2736:978-0-387-95231-4
2695:978-0-471-68029-1
2659:978-0-387-96098-2
2469:978-3-540-42669-1
2435:978-3-540-63061-6
2359:Wald, A. (1950).
2260:W. Edwards Deming
2176:{\displaystyle a}
1886:
1857:
1783:
1729:
1711:
1710:
1681:
1612:
1579:
1516:
1489:
1397:
1357:
1329:of the estimate,
1299:
1272:
1223:
498:
451:
422:
396:0-1 loss function
382:0-1 loss function
341:linear regression
204:Leonard J. Savage
156:in the 1920s. In
150:actuarial science
64:
63:
59:
16:(Redirected from
6256:
6221:Machine learning
6211:
6210:
6191:
5946:Action selection
5936:Self-driving car
5743:Stable Diffusion
5708:Speech synthesis
5673:
5537:Machine learning
5413:Gradient descent
5334:
5327:
5320:
5311:
5295:
5294:
5283:
5282:
5272:
5271:
5257:
5256:
5160:Crime statistics
5054:
5041:
4958:
4924:Fourier analysis
4911:Frequency domain
4891:
4838:
4804:Structural break
4764:
4713:Cluster analysis
4660:Log-linear model
4633:
4608:
4549:
4523:Homoscedasticity
4379:
4355:
4274:
4266:
4258:
4257:(KruskalâWallis)
4242:
4227:
4182:Cross validation
4167:
4149:AndersonâDarling
4096:
4083:
4054:Likelihood-ratio
4046:Parametric tests
4024:Permutation test
4007:1- & 2-tails
3898:Minimum distance
3870:Point estimation
3866:
3817:Optimal decision
3768:
3667:
3654:
3636:Quasi-experiment
3586:Adaptive designs
3437:
3424:
3301:Rank correlation
3063:
3054:
3041:
3008:
3001:
2994:
2985:
2980:
2949:
2926:
2899:
2866:Berger, James O.
2861:
2835:
2816:
2815:
2797:
2791:
2789:
2780:
2774:
2773:
2755:
2749:
2748:
2714:
2708:
2707:
2678:
2672:
2671:
2636:Berger, James O.
2632:
2626:
2625:
2608:
2602:
2601:
2577:
2571:
2570:
2550:
2544:
2543:
2515:
2509:
2508:
2480:
2474:
2473:
2446:
2440:
2439:
2412:
2406:
2405:
2403:
2401:
2388:
2382:
2381:
2373:
2367:
2366:
2356:
2350:
2349:
2324:Hastie, Trevor;
2321:
2302:Statistical risk
2239:
2237:
2236:
2231:
2226:
2225:
2209:
2204:
2182:
2180:
2179:
2174:
2158:
2156:
2155:
2150:
2132:
2130:
2129:
2124:
2122:
2114:
2083:
2081:
2080:
2075:
2073:
2072:
2012:in the field of
1999:utility function
1953:
1951:
1950:
1945:
1902:
1901:
1884:
1883:
1878:
1825:
1824:
1809:
1804:
1760:
1758:
1757:
1752:
1727:
1725:
1708:
1707:
1702:
1638:
1636:
1635:
1630:
1624:
1623:
1614:
1613:
1605:
1581:
1580:
1572:
1547:
1545:
1544:
1539:
1532:
1527:
1518:
1517:
1509:
1491:
1490:
1482:
1422:
1420:
1419:
1414:
1409:
1408:
1399:
1398:
1390:
1375:
1374:
1359:
1358:
1350:
1324:
1322:
1321:
1316:
1311:
1310:
1301:
1300:
1292:
1274:
1273:
1265:
1235:
1233:
1232:
1227:
1225:
1224:
1216:
1190:is known as the
1169:
1158:
1156:
1155:
1150:
1145:
1144:
1132:
1123:
1122:
1107:
1106:
1097:
1085:
1084:
1060:
1059:
1050:
1049:
1048:
1026:
1025:
1016:
1001:
1000:
988:
976:
975:
951:
950:
949:
939:
938:
917:
916:
887:
839:
837:
836:
831:
829:
828:
797:
795:
794:
789:
775:
774:
765:
759:
758:
734:
733:
724:
723:
711:
710:
686:
685:
673:
672:
542:Andranik Tangian
516:
514:
513:
508:
500:
499:
491:
474:
472:
471:
466:
464:
460:
453:
452:
444:
424:
423:
415:
300:
298:
297:
292:
289:
288:
115:fitness function
111:utility function
55:
35:
34:
27:
21:
6264:
6263:
6259:
6258:
6257:
6255:
6254:
6253:
6234:
6233:
6232:
6227:
6179:
6093:
6059:Google DeepMind
6037:
6003:Geoffrey Hinton
5962:
5899:
5825:Project Debater
5771:
5669:Implementations
5664:
5618:
5582:
5525:
5467:Backpropagation
5401:
5387:Tensor calculus
5341:
5338:
5308:
5303:
5266:
5237:
5199:
5136:
5122:quality control
5089:
5071:Clinical trials
5048:
5023:
5007:
4995:Hazard function
4989:
4943:
4905:
4889:
4852:
4848:BreuschâGodfrey
4836:
4813:
4753:
4728:Factor analysis
4674:
4655:Graphical model
4627:
4594:
4561:
4547:
4527:
4481:
4448:
4410:
4373:
4372:
4341:
4285:
4272:
4264:
4256:
4240:
4225:
4204:Rank statistics
4198:
4177:Model selection
4165:
4123:Goodness of fit
4117:
4094:
4068:
4040:
3993:
3938:
3927:Median unbiased
3855:
3766:
3699:Order statistic
3661:
3640:
3607:
3581:
3533:
3488:
3431:
3429:Data collection
3410:
3322:
3277:
3251:
3229:
3189:
3141:
3058:Continuous data
3048:
3035:
3017:
3012:
2969:10.2307/1911380
2954:
2931:
2904:
2888:
2864:
2833:
2828:
2825:
2823:Further reading
2820:
2819:
2812:
2799:
2798:
2794:
2783:
2781:
2777:
2770:
2757:
2756:
2752:
2737:
2716:
2715:
2711:
2696:
2682:DeGroot, Morris
2680:
2679:
2675:
2660:
2634:
2633:
2629:
2610:
2609:
2605:
2579:
2578:
2574:
2552:
2551:
2547:
2517:
2516:
2512:
2482:
2481:
2477:
2470:
2448:
2447:
2443:
2436:
2414:
2413:
2409:
2399:
2397:
2390:
2389:
2385:
2375:
2374:
2370:
2358:
2357:
2353:
2346:
2323:
2322:
2315:
2310:
2277:Bayesian regret
2273:
2217:
2185:
2184:
2165:
2164:
2135:
2134:
2090:
2089:
2064:
2044:
2043:
1960:
1887:
1810:
1777:
1776:
1675:
1674:
1658:
1645:
1615:
1553:
1552:
1463:
1462:
1400:
1366:
1331:
1330:
1302:
1246:
1245:
1209:
1208:
1200:
1167:
1098:
1051:
1039:
1017:
940:
930:
908:
897:
896:
885:
879:
852:
820:
815:
814:
766:
715:
664:
638:
637:
612:
598:
578:
566:
560:
529:
523:
484:
483:
480:Iverson bracket
441:
437:
402:
401:
392:decision theory
384:
280:
245:
244:
222:
201:
195:
190:
158:optimal control
107:profit function
103:reward function
75:decision theory
67:
60:
36:
32:
23:
22:
15:
12:
11:
5:
6262:
6260:
6252:
6251:
6249:Loss functions
6246:
6236:
6235:
6229:
6228:
6226:
6225:
6224:
6223:
6218:
6205:
6204:
6203:
6198:
6184:
6181:
6180:
6178:
6177:
6172:
6167:
6162:
6157:
6152:
6147:
6142:
6137:
6132:
6127:
6122:
6117:
6112:
6107:
6101:
6099:
6095:
6094:
6092:
6091:
6086:
6081:
6076:
6071:
6066:
6061:
6056:
6051:
6045:
6043:
6039:
6038:
6036:
6035:
6033:Ilya Sutskever
6030:
6025:
6020:
6015:
6010:
6005:
6000:
5998:Demis Hassabis
5995:
5990:
5988:Ian Goodfellow
5985:
5980:
5974:
5972:
5968:
5967:
5964:
5963:
5961:
5960:
5955:
5954:
5953:
5943:
5938:
5933:
5928:
5923:
5918:
5913:
5907:
5905:
5901:
5900:
5898:
5897:
5892:
5887:
5882:
5877:
5872:
5867:
5862:
5857:
5852:
5847:
5842:
5837:
5832:
5827:
5822:
5817:
5816:
5815:
5805:
5800:
5795:
5790:
5785:
5779:
5777:
5773:
5772:
5770:
5769:
5764:
5763:
5762:
5757:
5747:
5746:
5745:
5740:
5735:
5725:
5720:
5715:
5710:
5705:
5700:
5695:
5690:
5685:
5679:
5677:
5670:
5666:
5665:
5663:
5662:
5657:
5652:
5647:
5642:
5637:
5632:
5626:
5624:
5620:
5619:
5617:
5616:
5611:
5606:
5601:
5596:
5590:
5588:
5584:
5583:
5581:
5580:
5579:
5578:
5571:Language model
5568:
5563:
5558:
5557:
5556:
5546:
5545:
5544:
5533:
5531:
5527:
5526:
5524:
5523:
5521:Autoregression
5518:
5513:
5512:
5511:
5501:
5499:Regularization
5496:
5495:
5494:
5489:
5484:
5474:
5469:
5464:
5462:Loss functions
5459:
5454:
5449:
5444:
5439:
5438:
5437:
5427:
5422:
5421:
5420:
5409:
5407:
5403:
5402:
5400:
5399:
5397:Inductive bias
5394:
5389:
5384:
5379:
5374:
5369:
5364:
5359:
5351:
5349:
5343:
5342:
5339:
5337:
5336:
5329:
5322:
5314:
5305:
5304:
5302:
5301:
5289:
5277:
5263:
5250:
5247:
5246:
5243:
5242:
5239:
5238:
5236:
5235:
5230:
5225:
5220:
5215:
5209:
5207:
5201:
5200:
5198:
5197:
5192:
5187:
5182:
5177:
5172:
5167:
5162:
5157:
5152:
5146:
5144:
5138:
5137:
5135:
5134:
5129:
5124:
5115:
5110:
5105:
5099:
5097:
5091:
5090:
5088:
5087:
5082:
5077:
5068:
5066:Bioinformatics
5062:
5060:
5050:
5049:
5044:
5037:
5036:
5033:
5032:
5029:
5028:
5025:
5024:
5022:
5021:
5015:
5013:
5009:
5008:
5006:
5005:
4999:
4997:
4991:
4990:
4988:
4987:
4982:
4977:
4972:
4966:
4964:
4955:
4949:
4948:
4945:
4944:
4942:
4941:
4936:
4931:
4926:
4921:
4915:
4913:
4907:
4906:
4904:
4903:
4898:
4893:
4885:
4880:
4875:
4874:
4873:
4871:partial (PACF)
4862:
4860:
4854:
4853:
4851:
4850:
4845:
4840:
4832:
4827:
4821:
4819:
4818:Specific tests
4815:
4814:
4812:
4811:
4806:
4801:
4796:
4791:
4786:
4781:
4776:
4770:
4768:
4761:
4755:
4754:
4752:
4751:
4750:
4749:
4748:
4747:
4732:
4731:
4730:
4720:
4718:Classification
4715:
4710:
4705:
4700:
4695:
4690:
4684:
4682:
4676:
4675:
4673:
4672:
4667:
4665:McNemar's test
4662:
4657:
4652:
4647:
4641:
4639:
4629:
4628:
4611:
4604:
4603:
4600:
4599:
4596:
4595:
4593:
4592:
4587:
4582:
4577:
4571:
4569:
4563:
4562:
4560:
4559:
4543:
4537:
4535:
4529:
4528:
4526:
4525:
4520:
4515:
4510:
4505:
4503:Semiparametric
4500:
4495:
4489:
4487:
4483:
4482:
4480:
4479:
4474:
4469:
4464:
4458:
4456:
4450:
4449:
4447:
4446:
4441:
4436:
4431:
4426:
4420:
4418:
4412:
4411:
4409:
4408:
4403:
4398:
4393:
4387:
4385:
4375:
4374:
4371:
4370:
4365:
4359:
4358:
4351:
4350:
4347:
4346:
4343:
4342:
4340:
4339:
4338:
4337:
4327:
4322:
4317:
4316:
4315:
4310:
4299:
4297:
4291:
4290:
4287:
4286:
4284:
4283:
4278:
4277:
4276:
4268:
4260:
4244:
4241:(MannâWhitney)
4236:
4235:
4234:
4221:
4220:
4219:
4208:
4206:
4200:
4199:
4197:
4196:
4195:
4194:
4189:
4184:
4174:
4169:
4166:(ShapiroâWilk)
4161:
4156:
4151:
4146:
4141:
4133:
4127:
4125:
4119:
4118:
4116:
4115:
4107:
4098:
4086:
4080:
4078:Specific tests
4074:
4073:
4070:
4069:
4067:
4066:
4061:
4056:
4050:
4048:
4042:
4041:
4039:
4038:
4033:
4032:
4031:
4021:
4020:
4019:
4009:
4003:
4001:
3995:
3994:
3992:
3991:
3990:
3989:
3984:
3974:
3969:
3964:
3959:
3954:
3948:
3946:
3940:
3939:
3937:
3936:
3931:
3930:
3929:
3924:
3923:
3922:
3917:
3902:
3901:
3900:
3895:
3890:
3885:
3874:
3872:
3863:
3857:
3856:
3854:
3853:
3848:
3843:
3842:
3841:
3831:
3826:
3825:
3824:
3814:
3813:
3812:
3807:
3802:
3792:
3787:
3782:
3781:
3780:
3775:
3770:
3754:
3753:
3752:
3747:
3742:
3732:
3731:
3730:
3725:
3715:
3714:
3713:
3703:
3702:
3701:
3691:
3686:
3681:
3675:
3673:
3663:
3662:
3657:
3650:
3649:
3646:
3645:
3642:
3641:
3639:
3638:
3633:
3628:
3623:
3617:
3615:
3609:
3608:
3606:
3605:
3600:
3595:
3589:
3587:
3583:
3582:
3580:
3579:
3574:
3569:
3564:
3559:
3554:
3549:
3543:
3541:
3535:
3534:
3532:
3531:
3529:Standard error
3526:
3521:
3516:
3515:
3514:
3509:
3498:
3496:
3490:
3489:
3487:
3486:
3481:
3476:
3471:
3466:
3461:
3459:Optimal design
3456:
3451:
3445:
3443:
3433:
3432:
3427:
3420:
3419:
3416:
3415:
3412:
3411:
3409:
3408:
3403:
3398:
3393:
3388:
3383:
3378:
3373:
3368:
3363:
3358:
3353:
3348:
3343:
3338:
3332:
3330:
3324:
3323:
3321:
3320:
3315:
3314:
3313:
3308:
3298:
3293:
3287:
3285:
3279:
3278:
3276:
3275:
3270:
3265:
3259:
3257:
3256:Summary tables
3253:
3252:
3250:
3249:
3243:
3241:
3235:
3234:
3231:
3230:
3228:
3227:
3226:
3225:
3220:
3215:
3205:
3199:
3197:
3191:
3190:
3188:
3187:
3182:
3177:
3172:
3167:
3162:
3157:
3151:
3149:
3143:
3142:
3140:
3139:
3134:
3129:
3128:
3127:
3122:
3117:
3112:
3107:
3102:
3097:
3092:
3090:Contraharmonic
3087:
3082:
3071:
3069:
3060:
3050:
3049:
3044:
3037:
3036:
3034:
3033:
3028:
3022:
3019:
3018:
3013:
3011:
3010:
3003:
2996:
2988:
2982:
2981:
2951:
2950:
2940:(4): 489â504.
2928:
2927:
2901:
2900:
2886:
2862:
2844:(2): 413â437.
2824:
2821:
2818:
2817:
2810:
2792:
2775:
2768:
2750:
2735:
2709:
2694:
2673:
2658:
2627:
2603:
2592:(2): 103â122.
2572:
2561:(2): 409â428.
2545:
2526:(2): 476â512.
2510:
2491:(3): 608â640.
2475:
2468:
2441:
2434:
2407:
2383:
2368:
2351:
2344:
2312:
2311:
2309:
2306:
2305:
2304:
2299:
2294:
2289:
2284:
2279:
2272:
2269:
2229:
2224:
2220:
2216:
2213:
2208:
2203:
2200:
2197:
2193:
2172:
2148:
2145:
2142:
2121:
2117:
2113:
2109:
2106:
2103:
2100:
2097:
2071:
2067:
2063:
2060:
2057:
2054:
2051:
2033:differentiable
1959:
1956:
1955:
1954:
1943:
1940:
1937:
1933:
1930:
1927:
1924:
1920:
1917:
1914:
1911:
1908:
1905:
1900:
1897:
1894:
1890:
1881:
1877:
1874:
1871:
1867:
1864:
1861:
1855:
1852:
1849:
1846:
1843:
1840:
1837:
1834:
1831:
1828:
1823:
1820:
1817:
1813:
1807:
1803:
1800:
1797:
1793:
1790:
1787:
1773:expected value
1769:
1761:
1750:
1747:
1744:
1741:
1738:
1735:
1732:
1724:
1721:
1718:
1714:
1705:
1701:
1698:
1695:
1691:
1688:
1685:
1657:
1656:Decision rules
1654:
1644:
1641:
1640:
1639:
1627:
1622:
1618:
1611:
1608:
1602:
1599:
1596:
1593:
1590:
1587:
1584:
1578:
1575:
1569:
1566:
1563:
1560:
1537:
1531:
1526:
1522:
1515:
1512:
1506:
1503:
1500:
1497:
1494:
1488:
1485:
1479:
1476:
1473:
1470:
1452:function space
1436:
1431:estimates the
1412:
1407:
1403:
1396:
1393:
1387:
1384:
1381:
1378:
1373:
1369:
1365:
1362:
1356:
1353:
1347:
1344:
1341:
1338:
1314:
1309:
1305:
1298:
1295:
1289:
1286:
1283:
1280:
1277:
1271:
1268:
1262:
1259:
1256:
1253:
1222:
1219:
1199:
1196:
1180:Posterior Risk
1160:
1159:
1148:
1143:
1138:
1135:
1131:
1126:
1121:
1116:
1113:
1110:
1105:
1101:
1096:
1091:
1088:
1083:
1078:
1075:
1072:
1069:
1066:
1063:
1058:
1054:
1047:
1042:
1038:
1035:
1032:
1029:
1024:
1020:
1015:
1010:
1007:
1004:
999:
994:
991:
987:
982:
979:
974:
969:
966:
963:
960:
957:
954:
948:
943:
937:
933:
929:
926:
923:
920:
915:
911:
907:
904:
878:
875:
848:
827:
823:
799:
798:
787:
784:
781:
778:
773:
769:
764:
757:
752:
749:
746:
743:
740:
737:
732:
727:
722:
718:
714:
709:
704:
701:
698:
695:
692:
689:
684:
679:
676:
671:
667:
663:
660:
657:
654:
651:
648:
645:
608:
597:
594:
590:expected value
577:
574:
559:
556:
522:
519:
506:
503:
497:
494:
476:
475:
463:
459:
456:
450:
447:
440:
436:
433:
430:
427:
421:
418:
412:
409:
383:
380:
352:quadratic form
302:
301:
287:
283:
279:
276:
273:
270:
267:
264:
261:
258:
255:
252:
221:
218:
197:Main article:
194:
191:
189:
186:
146:classification
65:
62:
61:
39:
37:
30:
24:
14:
13:
10:
9:
6:
4:
3:
2:
6261:
6250:
6247:
6245:
6242:
6241:
6239:
6222:
6219:
6217:
6214:
6213:
6206:
6202:
6199:
6197:
6194:
6193:
6190:
6186:
6185:
6182:
6176:
6173:
6171:
6168:
6166:
6163:
6161:
6158:
6156:
6153:
6151:
6148:
6146:
6143:
6141:
6138:
6136:
6133:
6131:
6128:
6126:
6123:
6121:
6118:
6116:
6113:
6111:
6108:
6106:
6103:
6102:
6100:
6098:Architectures
6096:
6090:
6087:
6085:
6082:
6080:
6077:
6075:
6072:
6070:
6067:
6065:
6062:
6060:
6057:
6055:
6052:
6050:
6047:
6046:
6044:
6042:Organizations
6040:
6034:
6031:
6029:
6026:
6024:
6021:
6019:
6016:
6014:
6011:
6009:
6006:
6004:
6001:
5999:
5996:
5994:
5991:
5989:
5986:
5984:
5981:
5979:
5978:Yoshua Bengio
5976:
5975:
5973:
5969:
5959:
5958:Robot control
5956:
5952:
5949:
5948:
5947:
5944:
5942:
5939:
5937:
5934:
5932:
5929:
5927:
5924:
5922:
5919:
5917:
5914:
5912:
5909:
5908:
5906:
5902:
5896:
5893:
5891:
5888:
5886:
5883:
5881:
5878:
5876:
5875:Chinchilla AI
5873:
5871:
5868:
5866:
5863:
5861:
5858:
5856:
5853:
5851:
5848:
5846:
5843:
5841:
5838:
5836:
5833:
5831:
5828:
5826:
5823:
5821:
5818:
5814:
5811:
5810:
5809:
5806:
5804:
5801:
5799:
5796:
5794:
5791:
5789:
5786:
5784:
5781:
5780:
5778:
5774:
5768:
5765:
5761:
5758:
5756:
5753:
5752:
5751:
5748:
5744:
5741:
5739:
5736:
5734:
5731:
5730:
5729:
5726:
5724:
5721:
5719:
5716:
5714:
5711:
5709:
5706:
5704:
5701:
5699:
5696:
5694:
5691:
5689:
5686:
5684:
5681:
5680:
5678:
5674:
5671:
5667:
5661:
5658:
5656:
5653:
5651:
5648:
5646:
5643:
5641:
5638:
5636:
5633:
5631:
5628:
5627:
5625:
5621:
5615:
5612:
5610:
5607:
5605:
5602:
5600:
5597:
5595:
5592:
5591:
5589:
5585:
5577:
5574:
5573:
5572:
5569:
5567:
5564:
5562:
5559:
5555:
5554:Deep learning
5552:
5551:
5550:
5547:
5543:
5540:
5539:
5538:
5535:
5534:
5532:
5528:
5522:
5519:
5517:
5514:
5510:
5507:
5506:
5505:
5502:
5500:
5497:
5493:
5490:
5488:
5485:
5483:
5480:
5479:
5478:
5475:
5473:
5470:
5468:
5465:
5463:
5460:
5458:
5455:
5453:
5450:
5448:
5445:
5443:
5442:Hallucination
5440:
5436:
5433:
5432:
5431:
5428:
5426:
5423:
5419:
5416:
5415:
5414:
5411:
5410:
5408:
5404:
5398:
5395:
5393:
5390:
5388:
5385:
5383:
5380:
5378:
5375:
5373:
5370:
5368:
5365:
5363:
5360:
5358:
5357:
5353:
5352:
5350:
5348:
5344:
5335:
5330:
5328:
5323:
5321:
5316:
5315:
5312:
5300:
5299:
5290:
5288:
5287:
5278:
5276:
5275:
5270:
5264:
5262:
5261:
5252:
5251:
5248:
5234:
5231:
5229:
5228:Geostatistics
5226:
5224:
5221:
5219:
5216:
5214:
5211:
5210:
5208:
5206:
5202:
5196:
5195:Psychometrics
5193:
5191:
5188:
5186:
5183:
5181:
5178:
5176:
5173:
5171:
5168:
5166:
5163:
5161:
5158:
5156:
5153:
5151:
5148:
5147:
5145:
5143:
5139:
5133:
5130:
5128:
5125:
5123:
5119:
5116:
5114:
5111:
5109:
5106:
5104:
5101:
5100:
5098:
5096:
5092:
5086:
5083:
5081:
5078:
5076:
5072:
5069:
5067:
5064:
5063:
5061:
5059:
5058:Biostatistics
5055:
5051:
5047:
5042:
5038:
5020:
5019:Log-rank test
5017:
5016:
5014:
5010:
5004:
5001:
5000:
4998:
4996:
4992:
4986:
4983:
4981:
4978:
4976:
4973:
4971:
4968:
4967:
4965:
4963:
4959:
4956:
4954:
4950:
4940:
4937:
4935:
4932:
4930:
4927:
4925:
4922:
4920:
4917:
4916:
4914:
4912:
4908:
4902:
4899:
4897:
4894:
4892:
4890:(BoxâJenkins)
4886:
4884:
4881:
4879:
4876:
4872:
4869:
4868:
4867:
4864:
4863:
4861:
4859:
4855:
4849:
4846:
4844:
4843:DurbinâWatson
4841:
4839:
4833:
4831:
4828:
4826:
4825:DickeyâFuller
4823:
4822:
4820:
4816:
4810:
4807:
4805:
4802:
4800:
4799:Cointegration
4797:
4795:
4792:
4790:
4787:
4785:
4782:
4780:
4777:
4775:
4774:Decomposition
4772:
4771:
4769:
4765:
4762:
4760:
4756:
4746:
4743:
4742:
4741:
4738:
4737:
4736:
4733:
4729:
4726:
4725:
4724:
4721:
4719:
4716:
4714:
4711:
4709:
4706:
4704:
4701:
4699:
4696:
4694:
4691:
4689:
4686:
4685:
4683:
4681:
4677:
4671:
4668:
4666:
4663:
4661:
4658:
4656:
4653:
4651:
4648:
4646:
4645:Cohen's kappa
4643:
4642:
4640:
4638:
4634:
4630:
4626:
4622:
4618:
4614:
4609:
4605:
4591:
4588:
4586:
4583:
4581:
4578:
4576:
4573:
4572:
4570:
4568:
4564:
4558:
4554:
4550:
4544:
4542:
4539:
4538:
4536:
4534:
4530:
4524:
4521:
4519:
4516:
4514:
4511:
4509:
4506:
4504:
4501:
4499:
4498:Nonparametric
4496:
4494:
4491:
4490:
4488:
4484:
4478:
4475:
4473:
4470:
4468:
4465:
4463:
4460:
4459:
4457:
4455:
4451:
4445:
4442:
4440:
4437:
4435:
4432:
4430:
4427:
4425:
4422:
4421:
4419:
4417:
4413:
4407:
4404:
4402:
4399:
4397:
4394:
4392:
4389:
4388:
4386:
4384:
4380:
4376:
4369:
4366:
4364:
4361:
4360:
4356:
4352:
4336:
4333:
4332:
4331:
4328:
4326:
4323:
4321:
4318:
4314:
4311:
4309:
4306:
4305:
4304:
4301:
4300:
4298:
4296:
4292:
4282:
4279:
4275:
4269:
4267:
4261:
4259:
4253:
4252:
4251:
4248:
4247:Nonparametric
4245:
4243:
4237:
4233:
4230:
4229:
4228:
4222:
4218:
4217:Sample median
4215:
4214:
4213:
4210:
4209:
4207:
4205:
4201:
4193:
4190:
4188:
4185:
4183:
4180:
4179:
4178:
4175:
4173:
4170:
4168:
4162:
4160:
4157:
4155:
4152:
4150:
4147:
4145:
4142:
4140:
4138:
4134:
4132:
4129:
4128:
4126:
4124:
4120:
4114:
4112:
4108:
4106:
4104:
4099:
4097:
4092:
4088:
4087:
4084:
4081:
4079:
4075:
4065:
4062:
4060:
4057:
4055:
4052:
4051:
4049:
4047:
4043:
4037:
4034:
4030:
4027:
4026:
4025:
4022:
4018:
4015:
4014:
4013:
4010:
4008:
4005:
4004:
4002:
4000:
3996:
3988:
3985:
3983:
3980:
3979:
3978:
3975:
3973:
3970:
3968:
3965:
3963:
3960:
3958:
3955:
3953:
3950:
3949:
3947:
3945:
3941:
3935:
3932:
3928:
3925:
3921:
3918:
3916:
3913:
3912:
3911:
3908:
3907:
3906:
3903:
3899:
3896:
3894:
3891:
3889:
3886:
3884:
3881:
3880:
3879:
3876:
3875:
3873:
3871:
3867:
3864:
3862:
3858:
3852:
3849:
3847:
3844:
3840:
3837:
3836:
3835:
3832:
3830:
3827:
3823:
3822:loss function
3820:
3819:
3818:
3815:
3811:
3808:
3806:
3803:
3801:
3798:
3797:
3796:
3793:
3791:
3788:
3786:
3783:
3779:
3776:
3774:
3771:
3769:
3763:
3760:
3759:
3758:
3755:
3751:
3748:
3746:
3743:
3741:
3738:
3737:
3736:
3733:
3729:
3726:
3724:
3721:
3720:
3719:
3716:
3712:
3709:
3708:
3707:
3704:
3700:
3697:
3696:
3695:
3692:
3690:
3687:
3685:
3682:
3680:
3677:
3676:
3674:
3672:
3668:
3664:
3660:
3655:
3651:
3637:
3634:
3632:
3629:
3627:
3624:
3622:
3619:
3618:
3616:
3614:
3610:
3604:
3601:
3599:
3596:
3594:
3591:
3590:
3588:
3584:
3578:
3575:
3573:
3570:
3568:
3565:
3563:
3560:
3558:
3555:
3553:
3550:
3548:
3545:
3544:
3542:
3540:
3536:
3530:
3527:
3525:
3524:Questionnaire
3522:
3520:
3517:
3513:
3510:
3508:
3505:
3504:
3503:
3500:
3499:
3497:
3495:
3491:
3485:
3482:
3480:
3477:
3475:
3472:
3470:
3467:
3465:
3462:
3460:
3457:
3455:
3452:
3450:
3447:
3446:
3444:
3442:
3438:
3434:
3430:
3425:
3421:
3407:
3404:
3402:
3399:
3397:
3394:
3392:
3389:
3387:
3384:
3382:
3379:
3377:
3374:
3372:
3369:
3367:
3364:
3362:
3359:
3357:
3354:
3352:
3351:Control chart
3349:
3347:
3344:
3342:
3339:
3337:
3334:
3333:
3331:
3329:
3325:
3319:
3316:
3312:
3309:
3307:
3304:
3303:
3302:
3299:
3297:
3294:
3292:
3289:
3288:
3286:
3284:
3280:
3274:
3271:
3269:
3266:
3264:
3261:
3260:
3258:
3254:
3248:
3245:
3244:
3242:
3240:
3236:
3224:
3221:
3219:
3216:
3214:
3211:
3210:
3209:
3206:
3204:
3201:
3200:
3198:
3196:
3192:
3186:
3183:
3181:
3178:
3176:
3173:
3171:
3168:
3166:
3163:
3161:
3158:
3156:
3153:
3152:
3150:
3148:
3144:
3138:
3135:
3133:
3130:
3126:
3123:
3121:
3118:
3116:
3113:
3111:
3108:
3106:
3103:
3101:
3098:
3096:
3093:
3091:
3088:
3086:
3083:
3081:
3078:
3077:
3076:
3073:
3072:
3070:
3068:
3064:
3061:
3059:
3055:
3051:
3047:
3042:
3038:
3032:
3029:
3027:
3024:
3023:
3020:
3016:
3009:
3004:
3002:
2997:
2995:
2990:
2989:
2986:
2978:
2974:
2970:
2966:
2962:
2958:
2953:
2952:
2947:
2943:
2939:
2935:
2930:
2929:
2924:
2920:
2916:
2912:
2908:
2903:
2902:
2897:
2893:
2889:
2883:
2879:
2875:
2871:
2867:
2863:
2859:
2855:
2851:
2847:
2843:
2839:
2832:
2827:
2826:
2822:
2813:
2811:9780262541152
2807:
2803:
2796:
2793:
2787:
2779:
2776:
2771:
2765:
2761:
2754:
2751:
2746:
2742:
2738:
2732:
2728:
2724:
2720:
2713:
2710:
2705:
2701:
2697:
2691:
2687:
2683:
2677:
2674:
2669:
2665:
2661:
2655:
2651:
2647:
2643:
2642:
2637:
2631:
2628:
2624:
2620:
2619:
2614:
2607:
2604:
2599:
2595:
2591:
2587:
2583:
2576:
2573:
2568:
2564:
2560:
2556:
2549:
2546:
2541:
2537:
2533:
2529:
2525:
2521:
2514:
2511:
2506:
2502:
2498:
2494:
2490:
2486:
2479:
2476:
2471:
2465:
2461:
2457:
2453:
2445:
2442:
2437:
2431:
2427:
2423:
2419:
2411:
2408:
2396:
2395:
2387:
2384:
2379:
2372:
2369:
2364:
2363:
2355:
2352:
2347:
2345:0-387-95284-5
2341:
2337:
2336:
2331:
2327:
2320:
2318:
2314:
2307:
2303:
2300:
2298:
2295:
2293:
2290:
2288:
2285:
2283:
2280:
2278:
2275:
2274:
2270:
2268:
2265:
2261:
2257:
2255:
2249:
2247:
2243:
2222:
2218:
2211:
2206:
2201:
2198:
2195:
2191:
2170:
2162:
2146:
2143:
2140:
2115:
2107:
2101:
2095:
2087:
2086:absolute loss
2069:
2065:
2061:
2055:
2049:
2041:
2036:
2034:
2030:
2026:
2021:
2019:
2015:
2014:public health
2011:
2007:
2002:
2000:
1996:
1992:
1988:
1983:
1981:
1977:
1976:squared-error
1973:
1969:
1964:
1957:
1941:
1938:
1935:
1928:
1922:
1915:
1912:
1909:
1903:
1895:
1892:
1888:
1879:
1853:
1844:
1841:
1838:
1832:
1826:
1818:
1815:
1805:
1774:
1770:
1767:
1766:
1762:
1748:
1742:
1739:
1736:
1730:
1719:
1716:
1703:
1672:
1671:
1667:
1666:
1665:
1663:
1662:decision rule
1655:
1653:
1650:
1642:
1625:
1620:
1606:
1600:
1597:
1591:
1585:
1573:
1567:
1564:
1558:
1551:
1535:
1529:
1524:
1510:
1504:
1501:
1495:
1483:
1477:
1474:
1468:
1460:
1458:
1453:
1449:
1445:
1441:
1437:
1434:
1430:
1426:
1410:
1405:
1391:
1385:
1382:
1376:
1371:
1363:
1351:
1345:
1342:
1336:
1328:
1312:
1307:
1293:
1287:
1284:
1278:
1266:
1260:
1257:
1251:
1243:
1239:
1217:
1206:
1202:
1201:
1197:
1195:
1193:
1189:
1185:
1181:
1177:
1173:
1165:
1133:
1111:
1103:
1099:
1073:
1070:
1067:
1061:
1052:
1040:
1036:
1030:
1022:
1018:
1005:
989:
964:
961:
958:
952:
941:
931:
927:
921:
918:
913:
909:
902:
895:
894:
893:
891:
884:
876:
874:
872:
868:
864:
860:
856:
851:
847:
843:
825:
812:
808:
804:
785:
779:
771:
767:
747:
741:
738:
735:
725:
720:
716:
712:
699:
693:
690:
687:
677:
674:
669:
661:
655:
652:
649:
643:
636:
635:
634:
632:
628:
624:
620:
619:risk function
616:
611:
607:
603:
595:
593:
591:
587:
583:
575:
573:
571:
565:
558:Expected loss
557:
555:
552:
548:
543:
539:
538:Ragnar Frisch
535:
528:
520:
518:
504:
501:
492:
481:
461:
457:
454:
445:
438:
434:
428:
425:
416:
407:
400:
399:
398:
397:
393:
389:
381:
375:
371:
369:
365:
361:
357:
353:
349:
344:
342:
338:
337:least squares
334:
330:
326:
322:
317:
315:
311:
307:
285:
277:
274:
271:
265:
262:
256:
250:
243:
242:
241:
239:
235:
231:
230:least squares
227:
224:The use of a
219:
217:
215:
214:
209:
205:
200:
192:
187:
182:
178:
174:
169:
165:
163:
159:
155:
154:Harald CramĂŠr
151:
147:
143:
139:
138:economic cost
135:
131:
127:
123:
118:
116:
112:
108:
104:
100:
96:
92:
88:
84:
83:cost function
80:
79:loss function
76:
72:
58:
53:
49:
48:
43:
38:
29:
28:
19:
6064:Hugging Face
6028:David Silver
5676:Audioâvisual
5530:Applications
5509:Augmentation
5354:
5296:
5284:
5265:
5258:
5170:Econometrics
5120: /
5103:Chemometrics
5080:Epidemiology
5073: /
5046:Applications
4888:ARIMA model
4835:Q-statistic
4784:Stationarity
4680:Multivariate
4623: /
4619: /
4617:Multivariate
4615: /
4555: /
4551: /
4325:Bayes factor
4224:Signed rank
4136:
4110:
4102:
4090:
3821:
3785:Completeness
3621:Cohort study
3519:Opinion poll
3454:Missing data
3441:Study design
3396:Scatter plot
3318:Scatter plot
3311:Spearman's Ď
3273:Grouped data
2963:(1): 53â66.
2960:
2957:Econometrica
2956:
2937:
2933:
2917:(4): 43â59.
2914:
2910:
2869:
2841:
2837:
2801:
2795:
2785:
2778:
2759:
2753:
2718:
2712:
2685:
2676:
2640:
2630:
2616:
2606:
2589:
2585:
2575:
2558:
2554:
2548:
2523:
2519:
2513:
2488:
2484:
2478:
2450:
2444:
2416:
2410:
2398:. Retrieved
2393:
2386:
2377:
2371:
2361:
2354:
2334:
2297:Scoring rule
2258:
2250:
2245:
2241:
2040:squared loss
2037:
2022:
2003:
1987:risk neutral
1984:
1965:
1961:
1763:
1668:
1659:
1646:
1456:
1237:
1204:
1191:
1187:
1183:
1179:
1175:
1171:
1163:
1161:
889:
880:
870:
862:
858:
849:
845:
841:
806:
802:
800:
630:
626:
622:
618:
614:
609:
605:
599:
579:
569:
567:
530:
527:Scoring rule
477:
395:
385:
345:
323:, including
319:Many common
318:
313:
309:
305:
303:
237:
223:
211:
202:
130:Abraham Wald
119:
98:
82:
78:
68:
56:
47:Scoring rule
45:
6212:Categories
6160:Autoencoder
6115:Transformer
5983:Alex Graves
5931:OpenAI Five
5835:IBM Watsonx
5457:Convolution
5435:Overfitting
5298:WikiProject
5213:Cartography
5175:Jurimetrics
5127:Reliability
4858:Time domain
4837:(LjungâBox)
4759:Time-series
4637:Categorical
4621:Time-series
4613:Categorical
4548:(Bernoulli)
4383:Correlation
4363:Correlation
4159:JarqueâBera
4131:Chi-squared
3893:M-estimator
3846:Asymptotics
3790:Sufficiency
3557:Interaction
3469:Replication
3449:Effect size
3406:Violin plot
3386:Radar chart
3366:Forest plot
3356:Correlogram
3306:Kendall's Ď
2400:15 February
1995:risk-loving
1991:risk-averse
582:frequentist
91:real number
6238:Categories
6201:Technology
6054:EleutherAI
6013:Fei-Fei Li
6008:Yann LeCun
5921:Q-learning
5904:Decisional
5830:IBM Watson
5738:Midjourney
5630:TensorFlow
5477:Activation
5430:Regression
5425:Clustering
5165:Demography
4883:ARMA model
4688:Regression
4265:(Friedman)
4226:(Wilcoxon)
4164:Normality
4154:Lilliefors
4101:Student's
3977:Resampling
3851:Robustness
3839:divergence
3829:Efficiency
3767:(monotone)
3762:Likelihood
3679:Population
3512:Stratified
3464:Population
3283:Dependence
3239:Count data
3170:Percentile
3147:Dispersion
3080:Arithmetic
3015:Statistics
2308:References
2292:Hinge loss
2183:'s (as in
2084:, and the
2029:continuous
1765:Invariance
1176:Bayes Risk
877:Bayes Risk
811:population
576:Statistics
562:See also:
525:See also:
388:statistics
329:regression
321:statistics
181:Huber loss
6084:MIT CSAIL
6049:Anthropic
6018:Andrew Ng
5916:AlphaZero
5760:VideoPoet
5723:AlphaFold
5660:MindSpore
5614:SpiNNaker
5609:Memristor
5516:Diffusion
5492:Rectifier
5472:Batchnorm
5452:Attention
5447:Adversary
4546:Logistic
4313:posterior
4239:Rank sum
3987:Jackknife
3982:Bootstrap
3800:Bootstrap
3735:Parameter
3684:Statistic
3479:Statistic
3391:Run chart
3376:Pie chart
3371:Histogram
3361:Fan chart
3336:Bar chart
3218:L-moments
3105:Geometric
2684:(2004) .
2623:EMS Press
2192:∑
2023:For most
2010:morbidity
2006:mortality
1939:θ
1929:θ
1916:δ
1910:θ
1899:Θ
1896:∈
1893:θ
1889:∫
1880:δ
1845:δ
1839:θ
1827:
1822:Θ
1819:∈
1816:θ
1806:δ
1743:δ
1737:θ
1723:Θ
1720:∈
1717:θ
1704:δ
1617:‖
1610:^
1601:−
1595:‖
1592:
1577:^
1521:‖
1514:^
1505:−
1499:‖
1487:^
1425:Estimator
1395:^
1392:θ
1386:−
1383:θ
1377:
1372:θ
1355:^
1352:θ
1343:θ
1297:^
1294:θ
1288:−
1285:θ
1270:^
1267:θ
1258:θ
1221:^
1218:θ
1112:θ
1104:∗
1100:π
1068:θ
1057:Θ
1053:∫
1041:∫
1031:θ
1023:∗
1019:π
1006:θ
959:θ
942:∫
936:Θ
932:∫
914:∗
910:π
903:ρ
826:θ
772:θ
742:δ
736:θ
717:∫
694:δ
688:θ
675:
670:θ
656:δ
650:θ
502:≠
496:^
455:≠
449:^
420:^
356:tractable
275:−
251:λ
234:variances
226:quadratic
134:economics
6192:Portals
5951:Auto-GPT
5783:Word2vec
5587:Hardware
5504:Datasets
5406:Concepts
5260:Category
4953:Survival
4830:Johansen
4553:Binomial
4508:Isotonic
4095:(normal)
3740:location
3547:Blocking
3502:Sampling
3381:QâQ plot
3346:Box plot
3328:Graphics
3223:Skewness
3213:Kurtosis
3185:Variance
3115:Heronian
3110:Harmonic
2868:(1985).
2638:(1985).
2540:31019036
2505:39623350
2365:. Wiley.
2332:(2001).
2271:See also
2248:-value.
2161:outliers
1968:location
1435:'s mean.
869:of
586:Bayesian
551:cardinal
331:models,
188:Examples
6074:Meta AI
5911:AlphaGo
5895:PanGu-ÎŁ
5865:ChatGPT
5840:Granite
5788:Seq2seq
5767:Whisper
5688:WaveNet
5683:AlexNet
5655:Flux.jl
5635:PyTorch
5487:Sigmoid
5482:Softmax
5347:General
5286:Commons
5233:Kriging
5118:Process
5075:studies
4934:Wavelet
4767:General
3934:Plug-in
3728:L space
3507:Cluster
3208:Moments
3026:Outline
2977:1911380
2896:0804611
2874:Bibcode
2745:1835885
2704:2288194
2668:0804611
2646:Bibcode
1670:Minimax
867:support
547:ordinal
534:utility
325:t-tests
208:minimax
126:Laplace
52:Discuss
6089:Huawei
6069:OpenAI
5971:People
5941:MuZero
5803:Gemini
5798:Claude
5733:DALL-E
5645:Theano
5155:Census
4745:Normal
4693:Manova
4513:Robust
4263:2-way
4255:1-way
4093:-test
3764:
3341:Biplot
3132:Median
3125:Lehmer
3067:Center
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1980:median
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801:Here,
478:using
213:regret
193:Regret
144:. In
142:regret
42:merged
6155:Mamba
5926:SARSA
5890:LLaMA
5885:BLOOM
5870:GPT-J
5860:GPT-4
5855:GPT-3
5850:GPT-2
5845:GPT-1
5808:LaMDA
5640:Keras
4779:Trend
4308:prior
4250:anova
4139:-test
4113:-test
4105:-test
4012:Power
3957:Pivot
3750:shape
3745:scale
3195:Shape
3175:Range
3120:Heinz
3095:Cubic
3031:Index
2973:JSTOR
2834:(PDF)
2536:S2CID
2501:S2CID
853:is a
580:Both
368:Huber
87:event
44:into
6079:Mila
5880:PaLM
5813:Bard
5793:BERT
5776:Text
5755:Sora
5012:Test
4212:Sign
4064:Wald
3137:Mode
3075:Mean
2882:ISBN
2854:SSRN
2806:ISBN
2764:ISBN
2731:ISBN
2690:ISBN
2654:ISBN
2464:ISBN
2452:2000
2430:ISBN
2418:1995
2402:2021
2340:ISBN
2262:and
2031:and
1972:mean
1459:norm
1448:norm
584:and
390:and
177:SMAE
113:, a
109:, a
105:, a
77:, a
73:and
5820:NMT
5703:OCR
5698:HWR
5650:JAX
5604:VPU
5599:TPU
5594:IPU
5418:SGD
4192:BIC
4187:AIC
2965:doi
2942:doi
2919:doi
2846:doi
2723:doi
2594:doi
2563:doi
2559:157
2528:doi
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