2560:
1329:
2555:{\displaystyle {\begin{aligned}0&={\frac {\partial }{\partial \theta ^{\mathsf {T}}}}\operatorname {E} (s\mid \theta )\\&={\frac {\partial }{\partial \theta ^{\mathsf {T}}}}\int _{\mathcal {X}}{\frac {\partial \log {\mathcal {L}}(\theta ;X)}{\partial \theta }}f(x;\theta )\,dx\\&=\int _{\mathcal {X}}{\frac {\partial }{\partial \theta ^{\mathsf {T}}}}\left\{{\frac {\partial \log {\mathcal {L}}(\theta ;X)}{\partial \theta }}f(x;\theta )\right\}\,dx\\&=\int _{\mathcal {X}}\left\{{\frac {\partial ^{2}\log {\mathcal {L}}(\theta ;X)}{\partial \theta \,\partial \theta ^{\mathsf {T}}}}f(x;\theta )+{\frac {\partial \log {\mathcal {L}}(\theta ;X)}{\partial \theta }}{\frac {\partial f(x;\theta )}{\partial \theta ^{\mathsf {T}}}}\right\}\,dx\\&=\int _{\mathcal {X}}{\frac {\partial ^{2}\log {\mathcal {L}}(\theta ;X)}{\partial \theta \partial \theta ^{\mathsf {T}}}}f(x;\theta )\,dx+\int _{\mathcal {X}}{\frac {\partial \log {\mathcal {L}}(\theta ;X)}{\partial \theta }}{\frac {\partial f(x;\theta )}{\partial \theta ^{\mathsf {T}}}}\,dx\\&=\int _{\mathcal {X}}{\frac {\partial ^{2}\log {\mathcal {L}}(\theta ;X)}{\partial \theta \,\partial \theta ^{\mathsf {T}}}}f(x;\theta )\,dx+\int _{\mathcal {X}}{\frac {\partial \log {\mathcal {L}}(\theta ;X)}{\partial \theta }}{\frac {\partial \log {\mathcal {L}}(\theta ;X)}{\partial \theta ^{\mathsf {T}}}}f(x;\theta )\,dx\\&=\operatorname {E} \left({\frac {\partial ^{2}\log {\mathcal {L}}(\theta ;X)}{\partial \theta \,\partial \theta ^{\mathsf {T}}}}\right)+\operatorname {E} \left({\frac {\partial \log {\mathcal {L}}(\theta ;X)}{\partial \theta }}\left^{\mathsf {T}}\right)\end{aligned}}}
1081:
3562:
787:
3296:
1076:{\displaystyle {\begin{aligned}\operatorname {E} (s\mid \theta )&=\int _{\mathcal {X}}f(x;\theta ){\frac {\partial }{\partial \theta }}\log {\mathcal {L}}(\theta ;x)\,dx\\&=\int _{\mathcal {X}}f(x;\theta ){\frac {1}{f(x;\theta )}}{\frac {\partial f(x;\theta )}{\partial \theta }}\,dx=\int _{\mathcal {X}}{\frac {\partial f(x;\theta )}{\partial \theta }}\,dx\end{aligned}}}
3557:{\displaystyle {\begin{aligned}\operatorname {var} (s)&=\operatorname {var} \left({\frac {A}{\theta }}-{\frac {n-A}{1-\theta }}\right)=\operatorname {var} \left(A\left({\frac {1}{\theta }}+{\frac {1}{1-\theta }}\right)\right)\\&=\left({\frac {1}{\theta }}+{\frac {1}{1-\theta }}\right)^{2}\operatorname {var} (A)={\frac {n}{\theta (1-\theta )}}.\end{aligned}}}
3092:
2705:
4433:"score" or "efficient score" started to refer more commonly to the derivative of the log-likelihood function of the statistical model in question. This conceptual expansion was significantly influenced by a 1948 paper by C. R. Rao, which introduced "efficient score tests" that employed the derivative of the log-likelihood function.
4117:
4429:
the genetic abnormality being inherited. Fisher evaluated the efficacy of his scoring rule by comparing it with an alternative rule and against what he termed the "ideal score." The ideal score was defined as the derivative of the logarithm of the sampling density, as mentioned on page 193 of his work.
4428:
status as either homozygous or heterozygous. Fisher devised a method to assign each family a "score," calculated based on the number of children falling into each of the four categories. This score was used to estimate what he referred to as the "linkage parameter," which described the probability of
4414:
The term "score function" may initially seem unrelated to its contemporary meaning, which centers around the derivative of the log-likelihood function in statistical models. This apparent discrepancy can be traced back to the term's historical origins. The concept of the "score function" was first
389:
In older literature, "linear score" may refer to the score with respect to infinitesimal translation of a given density. This convention arises from a time when the primary parameter of interest was the mean or median of a distribution. In this case, the likelihood of an observation is given by a
4419:
in his 1935 paper titled "The
Detection of Linkage with 'Dominant' Abnormalities." Fisher employed the term in the context of genetic analysis, specifically for families where a parent had a dominant genetic abnormality. Over time, the application and meaning of the "score function" have evolved,
4432:
The term "score" later evolved through subsequent research, notably expanding beyond the specific application in genetics that Fisher had initially addressed. Various authors adapted Fisher's original methodology to more generalized statistical contexts. In these broader applications, the term
4423:
Fisher's initial use of the term was in the context of analyzing genetic attributes in families with a parent possessing a genetic abnormality. He categorized the children of such parents into four classes based on two binary traits: whether they had inherited the abnormality or not, and their
1187:
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309:
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4837:
Radhakrishna Rao, C. (1948). Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation. Mathematical
Proceedings of the Cambridge Philosophical Society, 44(1), 50-57.
4436:
Thus, what began as a specialized term in the realm of genetic statistics has evolved to become a fundamental concept in broader statistical theory, often associated with the derivative of the log-likelihood function.
3865:(such as a null-hypothesis value), in which case the result is a statistic. Intuitively, if the restricted estimator is near the maximum of the likelihood function, the score should not differ from zero by more than
531:
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792:
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637:
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448:
3087:{\displaystyle s={\frac {\partial \log {\mathcal {L}}}{\partial \theta }}={\frac {1}{\mathcal {L}}}{\frac {\partial {\mathcal {L}}}{\partial \theta }}={\frac {A}{\theta }}-{\frac {B}{1-\theta }}.}
2700:{\displaystyle \operatorname {E} (s(\theta )s(\theta )^{\mathsf {T}})=-\operatorname {E} \left({\frac {\partial ^{2}\log {\mathcal {L}}}{\partial \theta \,\partial \theta ^{\mathsf {T}}}}\right)}
3301:
191:
3667:
2745:
4766:
Yang Song; Jascha Sohl-Dickstein; Diederik P. Kingma; Abhishek Kumar; Stefano Ermon; Ben Poole (2020). "Score-Based
Generative Modeling through Stochastic Differential Equations".
4112:{\displaystyle -2\left=2\int _{\theta _{0}}^{\hat {\theta }}{\frac {d\,\log {\mathcal {L}}(\theta )}{d\theta }}\,d\theta =2\int _{\theta _{0}}^{\hat {\theta }}s(\theta )\,d\theta }
4404:
4176:
4406:, because it is not a likelihood function, neither it has a derivative with respect to the parameters. For more information about this definition, see the referenced paper.
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344:
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1210:
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is zero. Thus, if one were to repeatedly sample from some distribution, and repeatedly calculate the score, then the mean value of the scores would tend to zero
3742:
3248:
2765:
384:
3127:
647:. Under certain regularity conditions on the density functions of the random variables, the expected value of the score, evaluated at the true parameter value
4692:
Rao, C. Radhakrishna (1948). "Large sample tests of statistical hypotheses concerning several parameters with applications to problems of estimation".
4920:
456:
4825:
Miller, Jeff. "Earliest Known Uses of Some of the Words of
Mathematics (S)." Mathematics History Notes. Last revised on April 14, 2020.
4901:
4882:
4621:
4593:
4566:
4533:
1182:{\displaystyle {\frac {\partial }{\partial \theta }}\int _{\mathcal {X}}f(x;\theta )\,dx={\frac {\partial }{\partial \theta }}1=0.}
38:
3767:
569:
4214:
1213:
697:
393:
4866:
100:
4800:
Fisher, Ronald Aylmer. "The detection of linkage with 'dominant' abnormalities." Annals of
Eugenics 6.2 (1935): 187-201.
692:
4861:
151:
31:
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4197:
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107:
639:
at which the likelihood function is evaluated, and in view of the random character of sampling one may take its
3874:
2767:
has been averaged out. This concept of information is useful when comparing two methods of observation of some
2717:
68:
2747:. Note that the Fisher information is not a function of any particular observation, as the random variable
4647:
4364:
4122:
which means that the likelihood-ratio test can be understood as the area under the score function between
1192:
It is worth restating the above result in words: the expected value of the score, at true parameter value
4193:
3881:
1087:
72:
1316:{\displaystyle \operatorname {Var} (s(\theta ))=\operatorname {E} (s(\theta )s(\theta )^{\mathsf {T}})}
4152:
304:{\displaystyle s(\theta ;x)\equiv {\frac {\partial \log {\mathcal {L}}(\theta ;x)}{\partial \theta }}}
4703:
92:
4786:
2810:
760:
670:
198:
84:
4737:
Buse, A. (1982). "The
Likelihood Ratio, Wald, and Lagrange Multiplier Tests: An Expository Note".
3873:
first proved that the square of the score divided by the information matrix follows an asymptotic
4767:
4719:
4452:
4446:
4301:
4125:
3704:
3700:
2711:
1225:
317:
145:
4643:"Assessing the performance of prediction models. A framework for traditional and novel measures"
4856:
4558:
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4897:
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4529:
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194:
129:
96:
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3097:
We can now verify that the expectation of the score is zero. Noting that the expectation of
2948:{\displaystyle {\mathcal {L}}(\theta ;A,B)={\frac {(A+B)!}{A!B!}}\theta ^{A}(1-\theta )^{B},}
1195:
650:
549:
349:
208:
4852:
4748:
4711:
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4550:
4326:
4204:
386:, and indicates the sensitivity of the likelihood (its derivative normalized by its value).
125:
4826:
4187:
3573:
88:
3220:{\displaystyle E(s)={\frac {n\theta }{\theta }}-{\frac {n(1-\theta )}{1-\theta }}=n-n=0.}
4707:
1086:
The assumed regularity conditions allow the interchange of derivative and integral (see
4669:
4642:
4473:
4208:
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115:
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4723:
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80:
4810:
4752:
4609:
755:
644:
75:. Evaluated at a particular point of the parameter vector, the score indicates the
17:
4660:
4420:
diverging from its original context but retaining its foundational principles.
2565:
Hence the variance of the score is equal to the negative expected value of the
4715:
4458:
3842:
3719:
120:
52:
4476: ā How many standard deviations apart from the mean an observed datum is
3870:
3838:
3707:
76:
45:
4814:
4678:
4503:
4461: ā Statistical test based on the gradient of the likelihood function
4425:
1231:
526:{\displaystyle s_{\rm {linear}}={\frac {\partial }{\partial X}}\log f(X)}
141:
64:
4637:
Steyerberg, E. W.; Vickers, A. J.; Cook, N. R.; Gerds, T.; Gonen, M.;
3580:= 1 or 0), the model can be scored with the logarithm of predictions
103:
to find the parameter values that maximize the likelihood function.
4772:
1323:, can be derived from the above expression for the expected value.
124:
in which the parameter is held at a particular value. Further, the
83:
changes to the parameter values. If the log-likelihood function is
128:
evaluated at two distinct parameter values can be understood as a
44:
This article is about Score (statistics). Not to be confused with
4787:
https://www.jmlr.org/papers/volume6/hyvarinen05a/hyvarinen05a.pdf
4695:
Mathematical
Proceedings of the Cambridge Philosophical Society
4361:
It might seem confusing that the word score has been used for
79:
of the log-likelihood function and thereby the sensitivity to
4482: ā Function related to statistics and probability theory
4023:
3945:
3913:
3031:
3017:
2992:
2843:
2816:
2723:
2661:
2500:
2450:
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2220:
2200:
2119:
2092:
1994:
1974:
1894:
1867:
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1524:
1452:
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1121:
1021:
919:
876:
829:
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703:
676:
399:
270:
163:
4813:), Interpretation of "score", URL (version: 2019-04-17):
4827:
https://mathshistory.st-andrews.ac.uk/Miller/mathword/s/
3830:{\displaystyle \mathbf {x} =(x_{1},x_{2},\ldots ,x_{T})}
667:, is zero. To see this, rewrite the likelihood function
632:{\displaystyle \mathbf {x} =(x_{1},x_{2},\ldots ,x_{T})}
4484:
Pages displaying short descriptions of redirect targets
4262:{\displaystyle s_{\theta }\approx \nabla _{x}\log p(x)}
2800:
are failures, where the probability of success is
747:{\displaystyle {\mathcal {L}}(\theta ;x)=f(x;\theta )}
443:{\displaystyle {\mathcal {L}}(\theta ;X)=f(X+\theta )}
4367:
4335:
4304:
4275:
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4155:
4128:
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4469:
Pages displaying wikidata descriptions as a fallback
3676:
is the probability in the model to be estimated and
4582:Greenberg, Edward; Webster, Charles E. Jr. (1983).
4467: ā form of Newton's method used in statistics
4398:
4350:
4317:
4290:
4261:
4170:
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1090:), hence the above expression may be rewritten as
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378:
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303:
217:
185:
4585:Advanced Econometrics: A Bridge to the Literature
4553:Approximation Theorems of Mathematical Statistics
4203:Score matching describes the process of applying
3699:The scoring algorithm is an iterative method for
4811:https://stats.stackexchange.com/users/173082/ben
3845:, the score is evaluated at a specific value of
3841:. However, in certain applications, such as the
4588:. New York: John Wiley & Sons. p. 25.
4524:. Norwich: W. H. Hutchins & Sons. pp.
4455: ā Scientific study of digital information
186:{\displaystyle \log {\mathcal {L}}(\theta ;x)}
4796:
4794:
8:
4616:. Oxford: Basil Blackwell. pp. 16ā18.
4557:. New York: John Wiley & Sons. p.
3662:{\displaystyle S=Y\log(p)+(1-Y)(\log(1-p))}
4298:from finite samples. The learned function
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1993:
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4815:https://stats.stackexchange.com/q/342374
4641:; Pencina, M. J.; Kattan, M. W. (2010).
2796:of them are successes and the remaining
450:. The "linear score" is then defined as
4495:
3117:) , we can see that the expectation of
2740:{\displaystyle {\mathcal {I}}(\theta )}
4521:An Introduction to Likelihood Analysis
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2409:
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566:, it also depends on the observations
4896:. New York: Springer. Section 2.3.1.
4211:) to approximate the score function
106:Since the score is a function of the
7:
4399:{\displaystyle \nabla _{x}\log p(x)}
4873:Cox, D. R.; Hinkley, D. V. (1974).
4505:Informant in Encyclopaedia of Maths
4415:introduced by British statistician
3837:, so that, in general, it is not a
27:Gradient of the likelihood function
4369:
4232:
3230:We can also check the variance of
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2016:
1983:
1922:
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259:
25:
4614:Lectures on Advanced Econometrics
4182:Score matching (machine learning)
546:While the score is a function of
126:ratio of two likelihood functions
4171:{\displaystyle {\hat {\theta }}}
3772:
574:
4753:10.1080/00031305.1982.10482817
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2824:{\displaystyle {\mathcal {L}}}
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2011:
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774:{\displaystyle {\mathcal {X}}}
741:
729:
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708:
684:{\displaystyle {\mathcal {L}}}
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581:
520:
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333:
321:
314:This differentiation yields a
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250:
238:
205:-dimensional parameter vector
180:
168:
1:
4921:Maximum likelihood estimation
4838:doi:10.1017/S0305004100023987
2784:Consider observing the first
101:maximum likelihood estimation
4661:10.1097/EDE.0b013e3181c30fb2
4549:Serfling, Robert J. (1980).
4449: ā Notion in statistics
693:probability density function
346:row vector at each value of
4892:Schervish, Mark J. (1995).
4862:Encyclopedia of Mathematics
4318:{\displaystyle s_{\theta }}
4269:of an unknown distribution
4142:{\displaystyle \theta _{0}}
3877:under the null hypothesis.
3574:models with binary outcomes
2710:The latter is known as the
339:{\displaystyle (1\times m)}
4937:
4191:
4185:
3717:
3692:
1223:
43:
36:
32:Informant (disambiguation)
29:
4740:The American Statistician
4716:10.1017/S0305004100023987
4329:to draw new samples from
4198:Propensity score matching
4518:Pickles, Andrew (1985).
4351:{\displaystyle \pi (x)}
4291:{\displaystyle \pi (x)}
3858:{\displaystyle \theta }
3757:{\displaystyle \theta }
3105:and the expectation of
2569:of the log-likelihood.
1205:{\displaystyle \theta }
660:{\displaystyle \theta }
559:{\displaystyle \theta }
359:{\displaystyle \theta }
218:{\displaystyle \theta }
132:of the score function.
114:, it lends itself to a
110:, which are subject to
99:; this fact is used in
69:log-likelihood function
4877:. Chapman & Hall.
4875:Theoretical Statistics
4400:
4352:
4319:
4292:
4263:
4172:
4143:
4113:
3880:Further note that the
3859:
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3758:
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3274:) and the variance of
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1317:
1206:
1183:
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775:
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633:
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527:
444:
380:
360:
340:
305:
219:
187:
4401:
4353:
4320:
4293:
4264:
4207:algorithms (commonly
4194:Matching (statistics)
4173:
4144:
4114:
3882:likelihood-ratio test
3860:
3832:
3759:
3739:
3664:
3559:
3286:) so the variance of
3282:(1 −
3245:
3222:
3113:(1 −
3089:
2950:
2826:
2762:
2742:
2702:
2557:
1318:
1207:
1184:
1088:Leibniz integral rule
1078:
776:
749:
686:
662:
634:
561:
528:
445:
381:
361:
341:
306:
220:
201:, with respect to an
188:
4894:Theory of Statistics
4365:
4333:
4325:can then be used in
4302:
4273:
4215:
4192:For other uses, see
4153:
4126:
3891:
3849:
3768:
3764:and the observation
3748:
3728:
3587:
3568:Binary outcome model
3297:
3234:
3128:
2969:
2838:
2811:
2807:Then the likelihood
2751:
2718:
2576:
1330:
1238:
1196:
1097:
788:
761:
698:
671:
651:
570:
550:
457:
394:
390:density of the form
370:
350:
318:
232:
209:
152:
71:with respect to the
37:For other uses, see
30:For other uses, see
4708:1948PCPS...44...50R
4327:generative modeling
4089:
4007:
3270: −
199:likelihood function
146:partial derivatives
4453:Information theory
4447:Fisher information
4396:
4348:
4315:
4288:
4259:
4168:
4139:
4109:
4061:
3979:
3855:
3827:
3754:
3734:
3705:maximum likelihood
3659:
3554:
3552:
3240:
3217:
3084:
2945:
2821:
2792:, and seeing that
2757:
2737:
2712:Fisher information
2697:
2552:
2550:
1313:
1226:Fisher information
1202:
1179:
1073:
1071:
771:
744:
681:
657:
629:
556:
523:
440:
376:
356:
336:
301:
215:
183:
97:maximum or minimum
18:Score (statistics)
4465:Scoring algorithm
4165:
4086:
4046:
4004:
3962:
3744:is a function of
3737:{\displaystyle s}
3695:Scoring algorithm
3689:Scoring algorithm
3545:
3489:
3468:
3432:
3411:
3374:
3345:
3243:{\displaystyle s}
3197:
3159:
3079:
3058:
3045:
3021:
3006:
2908:
2790:Bernoulli process
2780:Bernoulli process
2760:{\displaystyle X}
2691:
2529:
2479:
2416:
2303:
2249:
2164:
2067:
2023:
1938:
1837:
1793:
1727:
1602:
1552:
1481:
1424:
1369:
1168:
1113:
1060:
1003:
968:
866:
754:, and denote the
503:
379:{\displaystyle x}
299:
195:natural logarithm
140:The score is the
130:definite integral
91:, the score will
16:(Redirected from
4928:
4907:
4888:
4869:
4839:
4835:
4829:
4823:
4817:
4807:
4801:
4798:
4789:
4784:
4778:
4777:
4775:
4763:
4757:
4756:
4734:
4728:
4727:
4689:
4683:
4682:
4672:
4634:
4628:
4627:
4606:
4600:
4599:
4579:
4573:
4572:
4556:
4546:
4540:
4539:
4515:
4509:
4508:
4500:
4485:
4470:
4405:
4403:
4402:
4397:
4377:
4376:
4357:
4355:
4354:
4349:
4324:
4322:
4321:
4316:
4314:
4313:
4297:
4295:
4294:
4289:
4268:
4266:
4265:
4260:
4240:
4239:
4227:
4226:
4205:machine learning
4177:
4175:
4174:
4169:
4167:
4166:
4158:
4148:
4146:
4145:
4140:
4138:
4137:
4118:
4116:
4115:
4110:
4088:
4087:
4079:
4076:
4075:
4074:
4047:
4045:
4037:
4027:
4026:
4009:
4006:
4005:
3997:
3994:
3993:
3992:
3972:
3968:
3964:
3963:
3955:
3949:
3948:
3930:
3929:
3917:
3916:
3864:
3862:
3861:
3856:
3836:
3834:
3833:
3828:
3823:
3822:
3804:
3803:
3791:
3790:
3775:
3763:
3761:
3760:
3755:
3743:
3741:
3740:
3735:
3703:determining the
3668:
3666:
3665:
3660:
3563:
3561:
3560:
3555:
3553:
3546:
3544:
3521:
3501:
3500:
3495:
3491:
3490:
3488:
3474:
3469:
3461:
3447:
3443:
3439:
3438:
3434:
3433:
3431:
3417:
3412:
3404:
3380:
3376:
3375:
3373:
3362:
3351:
3346:
3338:
3250:. We know that
3249:
3247:
3246:
3241:
3226:
3224:
3223:
3218:
3198:
3196:
3185:
3165:
3160:
3155:
3147:
3093:
3091:
3090:
3085:
3080:
3078:
3064:
3059:
3051:
3046:
3044:
3036:
3035:
3034:
3024:
3022:
3020:
3012:
3007:
3005:
2997:
2996:
2995:
2979:
2954:
2952:
2951:
2946:
2941:
2940:
2919:
2918:
2909:
2907:
2893:
2873:
2847:
2846:
2830:
2828:
2827:
2822:
2820:
2819:
2766:
2764:
2763:
2758:
2746:
2744:
2743:
2738:
2727:
2726:
2706:
2704:
2703:
2698:
2696:
2692:
2690:
2689:
2688:
2687:
2666:
2665:
2664:
2652:
2651:
2641:
2620:
2619:
2618:
2561:
2559:
2558:
2553:
2551:
2547:
2543:
2542:
2541:
2540:
2534:
2530:
2528:
2520:
2504:
2503:
2487:
2480:
2478:
2470:
2454:
2453:
2437:
2421:
2417:
2415:
2414:
2413:
2412:
2391:
2375:
2374:
2362:
2361:
2351:
2333:
2304:
2302:
2301:
2300:
2299:
2285:
2269:
2268:
2252:
2250:
2248:
2240:
2224:
2223:
2207:
2205:
2204:
2203:
2165:
2163:
2162:
2161:
2160:
2139:
2123:
2122:
2110:
2109:
2099:
2097:
2096:
2095:
2079:
2068:
2066:
2065:
2064:
2063:
2049:
2026:
2024:
2022:
2014:
1998:
1997:
1981:
1979:
1978:
1977:
1939:
1937:
1936:
1935:
1934:
1914:
1898:
1897:
1885:
1884:
1874:
1872:
1871:
1870:
1854:
1843:
1839:
1838:
1836:
1835:
1834:
1833:
1819:
1796:
1794:
1792:
1784:
1768:
1767:
1751:
1728:
1726:
1725:
1724:
1723:
1702:
1686:
1685:
1673:
1672:
1662:
1655:
1654:
1653:
1637:
1626:
1622:
1603:
1601:
1593:
1577:
1576:
1560:
1553:
1551:
1550:
1549:
1548:
1531:
1529:
1528:
1527:
1511:
1482:
1480:
1472:
1456:
1455:
1439:
1437:
1436:
1435:
1425:
1423:
1422:
1421:
1420:
1403:
1395:
1370:
1368:
1367:
1366:
1365:
1348:
1322:
1320:
1319:
1314:
1309:
1308:
1307:
1211:
1209:
1208:
1203:
1188:
1186:
1185:
1180:
1169:
1167:
1156:
1126:
1125:
1124:
1114:
1112:
1101:
1082:
1080:
1079:
1074:
1072:
1061:
1059:
1051:
1028:
1026:
1025:
1024:
1004:
1002:
994:
971:
969:
967:
944:
924:
923:
922:
906:
880:
879:
867:
865:
854:
834:
833:
832:
780:
778:
777:
772:
770:
769:
753:
751:
750:
745:
707:
706:
690:
688:
687:
682:
680:
679:
666:
664:
663:
658:
638:
636:
635:
630:
625:
624:
606:
605:
593:
592:
577:
565:
563:
562:
557:
532:
530:
529:
524:
504:
502:
491:
486:
485:
484:
449:
447:
446:
441:
403:
402:
385:
383:
382:
377:
365:
363:
362:
357:
345:
343:
342:
337:
310:
308:
307:
302:
300:
298:
290:
274:
273:
257:
224:
222:
221:
216:
192:
190:
189:
184:
167:
166:
73:parameter vector
21:
4936:
4935:
4931:
4930:
4929:
4927:
4926:
4925:
4911:
4910:
4904:
4891:
4885:
4872:
4851:
4848:
4843:
4842:
4836:
4832:
4824:
4820:
4808:
4804:
4799:
4792:
4785:
4781:
4765:
4764:
4760:
4747:(3a): 153ā157.
4736:
4735:
4731:
4691:
4690:
4686:
4636:
4635:
4631:
4624:
4608:
4607:
4603:
4596:
4581:
4580:
4576:
4569:
4548:
4547:
4543:
4536:
4517:
4516:
4512:
4502:
4501:
4497:
4492:
4483:
4468:
4443:
4412:
4368:
4363:
4362:
4331:
4330:
4305:
4300:
4299:
4271:
4270:
4231:
4218:
4213:
4212:
4209:neural networks
4201:
4190:
4188:Diffusion model
4184:
4151:
4150:
4129:
4124:
4123:
4066:
4038:
4010:
3984:
3921:
3904:
3900:
3889:
3888:
3847:
3846:
3814:
3795:
3782:
3766:
3765:
3746:
3745:
3726:
3725:
3722:
3716:
3697:
3691:
3686:
3585:
3584:
3570:
3551:
3550:
3525:
3478:
3459:
3455:
3454:
3445:
3444:
3421:
3402:
3398:
3394:
3390:
3363:
3352:
3336:
3332:
3319:
3295:
3294:
3232:
3231:
3186:
3166:
3148:
3126:
3125:
3068:
3037:
3025:
2998:
2980:
2967:
2966:
2932:
2910:
2894:
2874:
2836:
2835:
2809:
2808:
2782:
2777:
2749:
2748:
2716:
2715:
2714:and is written
2678:
2667:
2643:
2642:
2636:
2609:
2574:
2573:
2549:
2548:
2521:
2488:
2482:
2481:
2471:
2438:
2435:
2431:
2403:
2392:
2353:
2352:
2346:
2331:
2330:
2290:
2286:
2253:
2241:
2208:
2194:
2151:
2140:
2101:
2100:
2086:
2077:
2076:
2054:
2050:
2027:
2015:
1982:
1968:
1925:
1915:
1876:
1875:
1861:
1852:
1851:
1824:
1820:
1797:
1785:
1752:
1714:
1703:
1664:
1663:
1660:
1656:
1644:
1635:
1634:
1594:
1561:
1558:
1554:
1539:
1535:
1518:
1509:
1508:
1473:
1440:
1426:
1411:
1407:
1393:
1392:
1356:
1352:
1340:
1328:
1327:
1298:
1236:
1235:
1228:
1222:
1194:
1193:
1160:
1115:
1105:
1095:
1094:
1070:
1069:
1052:
1029:
1015:
995:
972:
948:
913:
904:
903:
858:
823:
816:
786:
785:
759:
758:
696:
695:
669:
668:
649:
648:
616:
597:
584:
568:
567:
548:
547:
544:
539:
495:
460:
455:
454:
392:
391:
368:
367:
348:
347:
316:
315:
291:
258:
230:
229:
207:
206:
204:
150:
149:
144:(the vector of
138:
89:parameter space
49:
42:
35:
28:
23:
22:
15:
12:
11:
5:
4934:
4932:
4924:
4923:
4913:
4912:
4909:
4908:
4902:
4889:
4883:
4870:
4853:Chentsov, N.N.
4847:
4844:
4841:
4840:
4830:
4818:
4802:
4790:
4779:
4758:
4729:
4684:
4655:(1): 128ā138.
4639:Obuchowski, N.
4629:
4622:
4601:
4594:
4574:
4567:
4541:
4534:
4510:
4494:
4493:
4491:
4488:
4487:
4486:
4477:
4474:Standard score
4471:
4462:
4456:
4450:
4442:
4439:
4411:
4408:
4395:
4392:
4389:
4386:
4383:
4380:
4375:
4371:
4347:
4344:
4341:
4338:
4312:
4308:
4287:
4284:
4281:
4278:
4258:
4255:
4252:
4249:
4246:
4243:
4238:
4234:
4230:
4225:
4221:
4183:
4180:
4164:
4161:
4136:
4132:
4120:
4119:
4108:
4105:
4101:
4098:
4095:
4092:
4085:
4082:
4073:
4069:
4064:
4060:
4057:
4054:
4051:
4044:
4041:
4036:
4033:
4030:
4025:
4020:
4017:
4013:
4003:
4000:
3991:
3987:
3982:
3978:
3975:
3971:
3967:
3961:
3958:
3952:
3947:
3942:
3939:
3936:
3933:
3928:
3924:
3920:
3915:
3910:
3907:
3903:
3899:
3896:
3875:Ļ-distribution
3867:sampling error
3854:
3826:
3821:
3817:
3813:
3810:
3807:
3802:
3798:
3794:
3789:
3785:
3781:
3778:
3774:
3753:
3733:
3718:Main article:
3715:
3712:
3693:Main article:
3690:
3687:
3685:
3682:
3680:is the score.
3670:
3669:
3658:
3655:
3652:
3649:
3646:
3643:
3640:
3637:
3634:
3631:
3628:
3625:
3622:
3619:
3616:
3613:
3610:
3607:
3604:
3601:
3598:
3595:
3592:
3569:
3566:
3565:
3564:
3549:
3543:
3540:
3537:
3534:
3531:
3528:
3524:
3519:
3516:
3513:
3510:
3507:
3504:
3499:
3494:
3487:
3484:
3481:
3477:
3472:
3467:
3464:
3458:
3453:
3450:
3448:
3446:
3442:
3437:
3430:
3427:
3424:
3420:
3415:
3410:
3407:
3401:
3397:
3393:
3389:
3386:
3383:
3379:
3372:
3369:
3366:
3361:
3358:
3355:
3349:
3344:
3341:
3335:
3331:
3328:
3325:
3322:
3320:
3318:
3315:
3312:
3309:
3306:
3303:
3302:
3239:
3228:
3227:
3216:
3213:
3210:
3207:
3204:
3201:
3195:
3192:
3189:
3184:
3181:
3178:
3175:
3172:
3169:
3163:
3158:
3154:
3151:
3145:
3142:
3139:
3136:
3133:
3095:
3094:
3083:
3077:
3074:
3071:
3067:
3062:
3057:
3054:
3049:
3043:
3040:
3033:
3028:
3019:
3015:
3010:
3004:
3001:
2994:
2989:
2986:
2983:
2977:
2974:
2956:
2955:
2944:
2939:
2935:
2931:
2928:
2925:
2922:
2917:
2913:
2906:
2903:
2900:
2897:
2892:
2889:
2886:
2883:
2880:
2877:
2871:
2868:
2865:
2862:
2859:
2856:
2853:
2850:
2845:
2818:
2781:
2778:
2776:
2773:
2769:random process
2756:
2736:
2733:
2730:
2725:
2708:
2707:
2695:
2686:
2681:
2677:
2673:
2670:
2663:
2658:
2655:
2650:
2646:
2639:
2635:
2632:
2629:
2626:
2623:
2617:
2612:
2608:
2605:
2602:
2599:
2596:
2593:
2590:
2587:
2584:
2581:
2567:Hessian matrix
2563:
2562:
2546:
2539:
2533:
2527:
2524:
2519:
2516:
2513:
2510:
2507:
2502:
2497:
2494:
2491:
2485:
2477:
2474:
2469:
2466:
2463:
2460:
2457:
2452:
2447:
2444:
2441:
2434:
2430:
2427:
2424:
2420:
2411:
2406:
2402:
2398:
2395:
2390:
2387:
2384:
2381:
2378:
2373:
2368:
2365:
2360:
2356:
2349:
2345:
2342:
2339:
2336:
2334:
2332:
2329:
2326:
2322:
2319:
2316:
2313:
2310:
2307:
2298:
2293:
2289:
2284:
2281:
2278:
2275:
2272:
2267:
2262:
2259:
2256:
2247:
2244:
2239:
2236:
2233:
2230:
2227:
2222:
2217:
2214:
2211:
2202:
2197:
2193:
2190:
2187:
2183:
2180:
2177:
2174:
2171:
2168:
2159:
2154:
2150:
2146:
2143:
2138:
2135:
2132:
2129:
2126:
2121:
2116:
2113:
2108:
2104:
2094:
2089:
2085:
2082:
2080:
2078:
2075:
2072:
2062:
2057:
2053:
2048:
2045:
2042:
2039:
2036:
2033:
2030:
2021:
2018:
2013:
2010:
2007:
2004:
2001:
1996:
1991:
1988:
1985:
1976:
1971:
1967:
1964:
1961:
1957:
1954:
1951:
1948:
1945:
1942:
1933:
1928:
1924:
1921:
1918:
1913:
1910:
1907:
1904:
1901:
1896:
1891:
1888:
1883:
1879:
1869:
1864:
1860:
1857:
1855:
1853:
1850:
1847:
1842:
1832:
1827:
1823:
1818:
1815:
1812:
1809:
1806:
1803:
1800:
1791:
1788:
1783:
1780:
1777:
1774:
1771:
1766:
1761:
1758:
1755:
1749:
1746:
1743:
1740:
1737:
1734:
1731:
1722:
1717:
1713:
1709:
1706:
1701:
1698:
1695:
1692:
1689:
1684:
1679:
1676:
1671:
1667:
1659:
1652:
1647:
1643:
1640:
1638:
1636:
1633:
1630:
1625:
1621:
1618:
1615:
1612:
1609:
1606:
1600:
1597:
1592:
1589:
1586:
1583:
1580:
1575:
1570:
1567:
1564:
1557:
1547:
1542:
1538:
1534:
1526:
1521:
1517:
1514:
1512:
1510:
1507:
1504:
1500:
1497:
1494:
1491:
1488:
1485:
1479:
1476:
1471:
1468:
1465:
1462:
1459:
1454:
1449:
1446:
1443:
1434:
1429:
1419:
1414:
1410:
1406:
1401:
1398:
1396:
1394:
1391:
1388:
1385:
1382:
1379:
1376:
1373:
1364:
1359:
1355:
1351:
1346:
1343:
1341:
1339:
1336:
1335:
1312:
1306:
1301:
1297:
1294:
1291:
1288:
1285:
1282:
1279:
1276:
1273:
1270:
1267:
1264:
1261:
1258:
1255:
1252:
1249:
1246:
1243:
1234:of the score,
1224:Main article:
1221:
1218:
1214:asymptotically
1201:
1190:
1189:
1178:
1175:
1172:
1166:
1163:
1159:
1154:
1151:
1148:
1144:
1141:
1138:
1135:
1132:
1129:
1123:
1118:
1111:
1108:
1104:
1084:
1083:
1068:
1065:
1058:
1055:
1050:
1047:
1044:
1041:
1038:
1035:
1032:
1023:
1018:
1014:
1011:
1008:
1001:
998:
993:
990:
987:
984:
981:
978:
975:
966:
963:
960:
957:
954:
951:
947:
942:
939:
936:
933:
930:
927:
921:
916:
912:
909:
907:
905:
902:
899:
895:
892:
889:
886:
883:
878:
873:
870:
864:
861:
857:
852:
849:
846:
843:
840:
837:
831:
826:
822:
819:
817:
815:
812:
809:
806:
803:
800:
797:
794:
793:
768:
743:
740:
737:
734:
731:
728:
725:
722:
719:
716:
713:
710:
705:
678:
656:
641:expected value
628:
623:
619:
615:
612:
609:
604:
600:
596:
591:
587:
583:
580:
576:
555:
543:
540:
538:
535:
534:
533:
522:
519:
516:
513:
510:
507:
501:
498:
494:
489:
483:
480:
477:
474:
471:
468:
463:
439:
436:
433:
430:
427:
424:
421:
418:
415:
412:
409:
406:
401:
375:
355:
335:
332:
329:
326:
323:
312:
311:
297:
294:
289:
286:
283:
280:
277:
272:
267:
264:
261:
255:
252:
249:
246:
243:
240:
237:
214:
202:
182:
179:
176:
173:
170:
165:
160:
157:
137:
134:
116:test statistic
112:sampling error
39:Score function
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
4933:
4922:
4919:
4918:
4916:
4905:
4903:0-387-94546-6
4899:
4895:
4890:
4886:
4884:0-412-12420-3
4880:
4876:
4871:
4868:
4864:
4863:
4858:
4854:
4850:
4849:
4845:
4834:
4831:
4828:
4822:
4819:
4816:
4812:
4806:
4803:
4797:
4795:
4791:
4788:
4783:
4780:
4774:
4769:
4762:
4759:
4754:
4750:
4746:
4742:
4741:
4733:
4730:
4725:
4721:
4717:
4713:
4709:
4705:
4701:
4697:
4696:
4688:
4685:
4680:
4676:
4671:
4666:
4662:
4658:
4654:
4650:
4649:
4644:
4640:
4633:
4630:
4625:
4623:0-631-14956-2
4619:
4615:
4611:
4610:Sargan, Denis
4605:
4602:
4597:
4595:0-471-09077-8
4591:
4587:
4586:
4578:
4575:
4570:
4568:0-471-02403-1
4564:
4560:
4555:
4554:
4545:
4542:
4537:
4535:0-86094-190-6
4531:
4527:
4523:
4522:
4514:
4511:
4507:
4506:
4499:
4496:
4489:
4481:
4480:Support curve
4478:
4475:
4472:
4466:
4463:
4460:
4457:
4454:
4451:
4448:
4445:
4444:
4440:
4438:
4434:
4430:
4427:
4421:
4418:
4417:Ronald Fisher
4409:
4407:
4390:
4384:
4381:
4378:
4373:
4359:
4342:
4336:
4328:
4310:
4306:
4282:
4276:
4253:
4247:
4244:
4241:
4236:
4228:
4223:
4219:
4210:
4206:
4199:
4195:
4189:
4181:
4179:
4159:
4134:
4130:
4106:
4103:
4096:
4090:
4080:
4071:
4067:
4062:
4058:
4055:
4052:
4049:
4042:
4039:
4031:
4018:
4015:
4011:
3998:
3989:
3985:
3980:
3976:
3973:
3969:
3956:
3940:
3937:
3934:
3926:
3922:
3908:
3905:
3901:
3897:
3894:
3887:
3886:
3885:
3883:
3878:
3876:
3872:
3868:
3852:
3844:
3840:
3819:
3815:
3811:
3808:
3805:
3800:
3796:
3792:
3787:
3783:
3776:
3751:
3731:
3721:
3713:
3711:
3709:
3706:
3702:
3696:
3688:
3683:
3681:
3679:
3675:
3650:
3647:
3644:
3638:
3635:
3626:
3623:
3620:
3614:
3608:
3602:
3599:
3596:
3593:
3590:
3583:
3582:
3581:
3579:
3575:
3567:
3547:
3538:
3535:
3532:
3526:
3522:
3517:
3511:
3505:
3502:
3497:
3492:
3485:
3482:
3479:
3475:
3470:
3465:
3462:
3456:
3451:
3449:
3440:
3435:
3428:
3425:
3422:
3418:
3413:
3408:
3405:
3399:
3395:
3391:
3387:
3384:
3381:
3377:
3370:
3367:
3364:
3359:
3356:
3353:
3347:
3342:
3339:
3333:
3329:
3326:
3323:
3321:
3313:
3307:
3304:
3293:
3292:
3291:
3289:
3285:
3281:
3277:
3273:
3269:
3265:
3261:
3257:
3253:
3237:
3214:
3211:
3208:
3205:
3202:
3199:
3193:
3190:
3187:
3179:
3176:
3173:
3167:
3161:
3156:
3152:
3149:
3143:
3137:
3131:
3124:
3123:
3122:
3120:
3116:
3112:
3108:
3104:
3100:
3081:
3075:
3072:
3069:
3065:
3060:
3055:
3052:
3047:
3041:
3013:
3008:
3002:
2987:
2984:
2975:
2972:
2965:
2964:
2963:
2961:
2958:so the score
2942:
2937:
2929:
2926:
2923:
2915:
2911:
2904:
2901:
2898:
2895:
2890:
2884:
2881:
2878:
2869:
2863:
2860:
2857:
2854:
2851:
2834:
2833:
2832:
2805:
2803:
2799:
2795:
2791:
2787:
2779:
2774:
2772:
2770:
2754:
2731:
2713:
2693:
2679:
2671:
2656:
2653:
2648:
2637:
2633:
2627:
2624:
2606:
2600:
2594:
2588:
2582:
2572:
2571:
2570:
2568:
2544:
2531:
2525:
2514:
2511:
2508:
2495:
2492:
2483:
2475:
2464:
2461:
2458:
2445:
2442:
2432:
2428:
2422:
2418:
2404:
2396:
2385:
2382:
2379:
2366:
2363:
2358:
2347:
2343:
2337:
2335:
2327:
2324:
2317:
2314:
2311:
2305:
2291:
2279:
2276:
2273:
2260:
2257:
2245:
2234:
2231:
2228:
2215:
2212:
2195:
2191:
2188:
2185:
2178:
2175:
2172:
2166:
2152:
2144:
2133:
2130:
2127:
2114:
2111:
2106:
2087:
2083:
2081:
2073:
2070:
2055:
2043:
2040:
2037:
2031:
2019:
2008:
2005:
2002:
1989:
1986:
1969:
1965:
1962:
1959:
1952:
1949:
1946:
1940:
1926:
1919:
1908:
1905:
1902:
1889:
1886:
1881:
1862:
1858:
1856:
1848:
1845:
1840:
1825:
1813:
1810:
1807:
1801:
1789:
1778:
1775:
1772:
1759:
1756:
1747:
1741:
1738:
1735:
1729:
1715:
1707:
1696:
1693:
1690:
1677:
1674:
1669:
1657:
1645:
1641:
1639:
1631:
1628:
1623:
1616:
1613:
1610:
1604:
1598:
1587:
1584:
1581:
1568:
1565:
1555:
1540:
1519:
1515:
1513:
1505:
1502:
1495:
1492:
1489:
1483:
1477:
1466:
1463:
1460:
1447:
1444:
1427:
1412:
1399:
1397:
1386:
1383:
1380:
1374:
1357:
1344:
1342:
1337:
1326:
1325:
1324:
1295:
1289:
1283:
1277:
1271:
1265:
1256:
1250:
1244:
1241:
1233:
1227:
1219:
1217:
1215:
1199:
1176:
1173:
1170:
1164:
1152:
1149:
1146:
1139:
1136:
1133:
1127:
1116:
1109:
1093:
1092:
1091:
1089:
1066:
1063:
1056:
1045:
1042:
1039:
1033:
1016:
1012:
1009:
1006:
999:
988:
985:
982:
976:
961:
958:
955:
949:
945:
937:
934:
931:
925:
914:
910:
908:
900:
897:
890:
887:
884:
871:
868:
862:
847:
844:
841:
835:
824:
820:
818:
810:
807:
804:
798:
784:
783:
782:
757:
738:
735:
732:
726:
723:
717:
714:
711:
694:
654:
646:
642:
621:
617:
613:
610:
607:
602:
598:
594:
589:
585:
578:
553:
541:
536:
517:
511:
508:
505:
499:
487:
461:
453:
452:
451:
434:
431:
428:
422:
419:
413:
410:
407:
387:
373:
353:
330:
327:
324:
295:
284:
281:
278:
265:
262:
253:
247:
244:
241:
235:
228:
227:
226:
212:
200:
196:
177:
174:
171:
158:
155:
147:
143:
135:
133:
131:
127:
123:
122:
117:
113:
109:
104:
102:
98:
94:
90:
86:
82:
81:infinitesimal
78:
74:
70:
66:
62:
58:
54:
47:
40:
33:
19:
4893:
4874:
4860:
4833:
4821:
4805:
4782:
4761:
4744:
4738:
4732:
4702:(1): 50ā57.
4699:
4693:
4687:
4652:
4648:Epidemiology
4646:
4632:
4613:
4604:
4584:
4577:
4552:
4544:
4520:
4513:
4504:
4498:
4435:
4431:
4422:
4413:
4360:
4202:
4121:
3884:is given by
3879:
3723:
3698:
3684:Applications
3677:
3673:
3671:
3577:
3571:
3287:
3283:
3279:
3275:
3271:
3267:
3263:
3259:
3255:
3251:
3229:
3118:
3114:
3110:
3106:
3102:
3098:
3096:
2959:
2957:
2806:
2801:
2797:
2793:
2788:trials of a
2785:
2783:
2709:
2564:
1229:
1191:
1085:
756:sample space
645:sample space
545:
388:
313:
139:
119:
108:observations
105:
60:
56:
50:
4857:"Informant"
3869:. In 1948,
3701:numerically
95:at a local
4846:References
4773:2011.13456
4459:Score test
4186:See also:
3843:score test
3724:Note that
3720:Score test
3714:Score test
537:Properties
136:Definition
121:score test
85:continuous
53:statistics
4867:EMS Press
4855:(2001) ,
4724:122382660
4382:
4370:∇
4337:π
4311:θ
4277:π
4245:
4233:∇
4229:≈
4224:θ
4163:^
4160:θ
4131:θ
4107:θ
4097:θ
4084:^
4081:θ
4068:θ
4063:∫
4053:θ
4043:θ
4032:θ
4019:
4002:^
3999:θ
3986:θ
3981:∫
3960:^
3957:θ
3941:
3935:−
3923:θ
3909:
3895:−
3871:C. R. Rao
3853:θ
3839:statistic
3809:…
3752:θ
3708:estimator
3648:−
3639:
3624:−
3603:
3539:θ
3536:−
3527:θ
3506:
3486:θ
3483:−
3466:θ
3429:θ
3426:−
3409:θ
3388:
3371:θ
3368:−
3357:−
3348:−
3343:θ
3330:
3308:
3206:−
3194:θ
3191:−
3180:θ
3177:−
3162:−
3157:θ
3153:θ
3076:θ
3073:−
3061:−
3056:θ
3042:θ
3039:∂
3027:∂
3003:θ
3000:∂
2988:
2982:∂
2930:θ
2927:−
2912:θ
2852:θ
2732:θ
2680:θ
2676:∂
2672:θ
2669:∂
2657:
2645:∂
2634:
2628:−
2607:θ
2595:θ
2583:
2526:θ
2523:∂
2509:θ
2496:
2490:∂
2476:θ
2473:∂
2459:θ
2446:
2440:∂
2429:
2405:θ
2401:∂
2397:θ
2394:∂
2380:θ
2367:
2355:∂
2344:
2318:θ
2292:θ
2288:∂
2274:θ
2261:
2255:∂
2246:θ
2243:∂
2229:θ
2216:
2210:∂
2196:∫
2179:θ
2153:θ
2149:∂
2145:θ
2142:∂
2128:θ
2115:
2103:∂
2088:∫
2056:θ
2052:∂
2044:θ
2029:∂
2020:θ
2017:∂
2003:θ
1990:
1984:∂
1970:∫
1953:θ
1927:θ
1923:∂
1920:θ
1917:∂
1903:θ
1890:
1878:∂
1863:∫
1826:θ
1822:∂
1814:θ
1799:∂
1790:θ
1787:∂
1773:θ
1760:
1754:∂
1742:θ
1716:θ
1712:∂
1708:θ
1705:∂
1691:θ
1678:
1666:∂
1646:∫
1617:θ
1599:θ
1596:∂
1582:θ
1569:
1563:∂
1541:θ
1537:∂
1533:∂
1520:∫
1496:θ
1478:θ
1475:∂
1461:θ
1448:
1442:∂
1428:∫
1413:θ
1409:∂
1405:∂
1387:θ
1384:∣
1375:
1358:θ
1354:∂
1350:∂
1296:θ
1284:θ
1272:
1257:θ
1245:
1200:θ
1165:θ
1162:∂
1158:∂
1140:θ
1117:∫
1110:θ
1107:∂
1103:∂
1057:θ
1054:∂
1046:θ
1031:∂
1017:∫
1000:θ
997:∂
989:θ
974:∂
962:θ
938:θ
915:∫
885:θ
872:
863:θ
860:∂
856:∂
848:θ
825:∫
811:θ
808:∣
799:
739:θ
712:θ
655:θ
643:over the
611:…
554:θ
509:
497:∂
493:∂
435:θ
408:θ
354:θ
328:×
296:θ
293:∂
279:θ
266:
260:∂
254:≡
242:θ
213:θ
172:θ
159:
118:known as
87:over the
77:steepness
63:) is the
61:informant
46:Raw score
4915:Category
4679:20010215
4612:(1988).
4441:See also
4426:zygosity
2775:Examples
1232:variance
1220:Variance
781:. Then:
142:gradient
65:gradient
4704:Bibcode
4670:3575184
4410:History
3266:=
197:of the
67:of the
4900:
4881:
4722:
4677:
4667:
4620:
4592:
4565:
4532:
3672:where
193:, the
93:vanish
55:, the
4809:Ben (
4768:arXiv
4720:S2CID
4526:24ā29
4490:Notes
691:as a
148:) of
57:score
4898:ISBN
4879:ISBN
4675:PMID
4618:ISBN
4590:ISBN
4563:ISBN
4530:ISBN
4196:and
4149:and
3572:For
3262:(so
1230:The
542:Mean
366:and
59:(or
4749:doi
4712:doi
4665:PMC
4657:doi
4559:145
4379:log
4242:log
4016:log
3938:log
3906:log
3636:log
3600:log
3503:var
3385:var
3327:var
3305:var
3290:is
3278:is
3121:is
3109:is
3101:is
2985:log
2962:is
2831:is
2654:log
2493:log
2443:log
2364:log
2258:log
2213:log
2112:log
1987:log
1887:log
1757:log
1675:log
1566:log
1445:log
1242:Var
869:log
506:log
263:log
156:log
51:In
4917::
4865:,
4859:,
4793:^
4745:36
4743:.
4718:.
4710:.
4700:44
4698:.
4673:.
4663:.
4653:21
4651:.
4645:.
4561:.
4528:.
4358:.
4178:.
3710:.
3280:nĪø
3258:=
3254:+
3215:0.
3103:nĪø
2804:.
2771:.
1216:.
1177:0.
225:.
4906:.
4887:.
4776:.
4770::
4755:.
4751::
4726:.
4714::
4706::
4681:.
4659::
4626:.
4598:.
4571:.
4538:.
4394:)
4391:x
4388:(
4385:p
4374:x
4346:)
4343:x
4340:(
4307:s
4286:)
4283:x
4280:(
4257:)
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4251:(
4248:p
4237:x
4220:s
4200:.
4135:0
4104:d
4100:)
4094:(
4091:s
4072:0
4059:2
4056:=
4050:d
4040:d
4035:)
4029:(
4024:L
4012:d
3990:0
3977:2
3974:=
3970:]
3966:)
3951:(
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3932:)
3927:0
3919:(
3914:L
3902:[
3898:2
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3642:(
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3612:)
3609:p
3606:(
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3576:(
3548:.
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3509:(
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3406:1
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3396:A
3392:(
3382:=
3378:)
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3334:(
3324:=
3317:)
3314:s
3311:(
3288:s
3284:Īø
3276:A
3272:A
3268:n
3264:B
3260:n
3256:B
3252:A
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3212:=
3209:n
3203:n
3200:=
3188:1
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3174:1
3171:(
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3150:n
3144:=
3141:)
3138:s
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3099:A
3082:.
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3048:=
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3009:=
2993:L
2976:=
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2960:s
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