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December2000 Asymptotic approximations for error probabilities of sequential or fixed sample size tests in exponential families
Hock Peng Chan, Tze Leung Lai
Ann. Statist. 28(6): 1638-1669 (December2000). DOI: 10.1214/aos/1015957474

Abstract

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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Hock Peng Chan. Tze Leung Lai. "Asymptotic approximations for error probabilities of sequential or fixed sample size tests in exponential families." Ann. Statist. 28 (6) 1638 - 1669, December2000. https://doi.org/10.1214/aos/1015957474

Information

Published: December2000
First available in Project Euclid: 12 March 2002

zbMATH: 1105.62367
MathSciNet: MR1835035
Digital Object Identifier: 10.1214/aos/1015957474

Subjects:
Primary: 62E20 , 62L10 , 62L15
Secondary: 49Q15 , 60F10

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

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 6 • December2000
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