Asymptotically uniformly most powerful tests in parametric and semiparametric models
Sungsub Choi, W. J. Hall, Anton Schick
The Annals of Statistics · 1996 · Volume 24 · Issue 2
Abstract
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.
Keywords
62F05; 62G20; Adaptation; asymptotic confidence sets; effective scores; efficient tests; Invariance; local alternatives; Unbiased tests;
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