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Asymptotic approximations for error probabilities of sequential or fixed sample size tests in exponential families. (English) Zbl 1105.62367

Summary: 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.

MSC:

62L10 Sequential statistical analysis
62B05 Sufficient statistics and fields
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