The Annals of Statistics

Asymptotically uniformly most powerful tests in parametric and semiparametric models

Sungsub Choi, W. J. Hall, and Anton Schick

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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.

Article information

Ann. Statist. Volume 24, Number 2 (1996), 841-861.

First available in Project Euclid: 24 September 2002

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F05: Asymptotic properties of tests
Secondary: 62G20: Asymptotic properties

Local alternatives effective scores unbiased tests invariance efficient tests adaptation asymptotic confidence sets


Choi, Sungsub; Hall, W. J.; Schick, Anton. Asymptotically uniformly most powerful tests in parametric and semiparametric models. Ann. Statist. 24 (1996), no. 2, 841--861. doi:10.1214/aos/1032894469.

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