The Annals of Statistics

Asymptotic approximations for error probabilities of sequential or fixed sample size tests in exponential families

Hock Peng Chan and Tze Leung Lai

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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.

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Ann. Statist., Volume 28, Number 6 (2000), 1638-1669.

First available in Project Euclid: 12 March 2002

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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]

Sequential generalized likelihood ratio tests Bayes sequential tests multiparameter exponential families boundary crossing probabilities integration over tubes


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.

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