Open Access
April 1996 Asymptotically uniformly most powerful tests in parametric and semiparametric models
Sungsub Choi, W. J. Hall, Anton Schick
Ann. Statist. 24(2): 841-861 (April 1996). DOI: 10.1214/aos/1032894469


Tests of hypotheses about finite-dimensional parameters in a semiparametric model are studied from Pitman's moving alternative (or local) approach using Le Cam's local asymptotic normality concept. For the case of a real parameter being tested, asymptotically uniformly most powerful (AUMP) tests are characterized for one-sided hypotheses, and AUMP unbiased tests for two-sided ones. An asymptotic invariance principle is introduced for multidimensional hypotheses, and AUMP invariant tests are characterized. These provide optimality for Wald, Rao (score), Neyman-Rao (effective score) and likelihood ratio tests in parametric models, and for Neyman-Rao tests in semiparametric models when constructions are feasible. Inversions lead to asymptotically uniformly most accurate confidence sets. Examples include one-, two- and k-sample problems, a linear regression model with unknown error distribution and a proportional hazards regression model with arbitrary baseline hazards. Results are presented in a format that facilitates application in strictly parametric models.


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Sungsub Choi. W. J. Hall. Anton Schick. "Asymptotically uniformly most powerful tests in parametric and semiparametric models." Ann. Statist. 24 (2) 841 - 861, April 1996.


Published: April 1996
First available in Project Euclid: 24 September 2002

zbMATH: 0860.62020
MathSciNet: MR1394992
Digital Object Identifier: 10.1214/aos/1032894469

Primary: 62F05
Secondary: 62G20

Keywords: Adaptation , asymptotic confidence sets , effective scores , efficient tests , Invariance , local alternatives , Unbiased tests

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 2 • April 1996
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