The Annals of Statistics
- Ann. Statist.
- Volume 28, Number 6 (2000), 1638-1669.
Asymptotic approximations for error probabilities of sequential or fixed sample size tests in exponential families
Asymptotic approximations for the error probabilities of sequential tests of composite hypotheses in multiparameter exponential families are developed herein for a general class of test statistics, including generalized likelihood ratio statistics and other functions of the sufficient statistics. These results not only generalize previous approximations for Type I error probabilities of sequential generalized likelihood ratio tests, but also pro- vide a unified treatment of both sequential and fixed sample size tests and of Type I and Type II error probabilities. Geometric arguments involving integration over tubes play an important role in this unified theory.
Ann. Statist., Volume 28, Number 6 (2000), 1638-1669.
First available in Project Euclid: 12 March 2002
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62L10: Sequential analysis 62L15: Optimal stopping [See also 60G40, 91A60] 62E20: Asymptotic distribution theory
Secondary: 60F10: Large deviations 49Q15: Geometric measure and integration theory, integral and normal currents [See also 28A75, 32C30, 58A25, 58C35]
Chan, Hock Peng; Lai, Tze Leung. Asymptotic approximations for error probabilities of sequential or fixed sample size tests in exponential families. Ann. Statist. 28 (2000), no. 6, 1638--1669. doi:10.1214/aos/1015957474. https://projecteuclid.org/euclid.aos/1015957474