The Annals of Statistics
- Ann. Statist.
- Volume 24, Number 2 (1996), 841-861.
Asymptotically uniformly most powerful tests in parametric and semiparametric models
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.
Ann. Statist. Volume 24, Number 2 (1996), 841-861.
First available in Project Euclid: 24 September 2002
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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. http://projecteuclid.org/euclid.aos/1032894469.