On some optimality properties of fisher-rao score function in testing and estimation

Anil K. Bera; Yannis Bilias

doi:10.1081/STA-100105683

On some optimality properties of fisher-rao score function in testing and estimation

Research output: Contribution to journal › Conference article › peer-review

Abstract

The score function is associated with some optimality features in statistical inference. This review article looks on the central role of the score in testing and estimation. The maximization of the power in testing and the quest for efficiency in estimation lead to score as a guiding principle. In hypothesis testing, the locally most powerful test statistic is the score test or a transformation of it. In estimation, the optimal estimating function is the score. The same link can be made in the case of nuisance parameters: the optimal test function should have maximum correlation with the score of the parameter of primary interest. We complement this result by showing that the same criterion should be satisfied in the estimation problem as well.

Original language	English (US)
Pages (from-to)	1533-1559
Number of pages	27
Journal	Communications in Statistics - Theory and Methods
Volume	30
Issue number	8-9
DOIs	https://doi.org/10.1081/STA-100105683
State	Published - 2001
Event	Statistics Reflections on the Past and Visions for the Future-International Conference in Honor of Prof. C.R. Rao on the Occasion of His 80th Birthday- - San Antonio, TX, United States Duration: Mar 16 2000 → Mar 19 2000

Keywords

Efficiency
Efficient method of moment
Estimating function
Locally most powerful test
Rao's score test
Score function

ASJC Scopus subject areas

Statistics and Probability

Online availability

10.1081/STA-100105683

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title = "On some optimality properties of fisher-rao score function in testing and estimation",

abstract = "The score function is associated with some optimality features in statistical inference. This review article looks on the central role of the score in testing and estimation. The maximization of the power in testing and the quest for efficiency in estimation lead to score as a guiding principle. In hypothesis testing, the locally most powerful test statistic is the score test or a transformation of it. In estimation, the optimal estimating function is the score. The same link can be made in the case of nuisance parameters: the optimal test function should have maximum correlation with the score of the parameter of primary interest. We complement this result by showing that the same criterion should be satisfied in the estimation problem as well.",

keywords = "Efficiency, Efficient method of moment, Estimating function, Locally most powerful test, Rao's score test, Score function",

author = "Bera, {Anil K.} and Yannis Bilias",

note = "Funding Information: This paper is based on an invited presentation at the international conference, Statistics: Reflections on the Past and Visions for the Future in honor of Professor C. R. Rao on the occasion of his 80th birthday, held at the University of Texas at San Antonio, March 16–19, 2000. We wish to thank the participants for helpful comments and discussion. We are grateful to an anonymous referee for many helpful suggestions that have considerably improved the paper. We would also like to thank Tatyana Dubovyk for providing very competent research assistance and to Naoko Miki for her help in preparing the manu script. However, we retain the responsibility for any remaining errors. Financial support from the Office of Research, College of Commerce and Business Administration, University of Illinois of Urbana-Champaign is gratefully acknowledged.; Statistics Reflections on the Past and Visions for the Future-International Conference in Honor of Prof. C.R. Rao on the Occasion of His 80th Birthday- ; Conference date: 16-03-2000 Through 19-03-2000",

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PY - 2001

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KW - Efficient method of moment

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KW - Locally most powerful test

KW - Rao's score test

KW - Score function

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On some optimality properties of fisher-rao score function in testing and estimation

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