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

• 成果类型: Article
• 署名作者: Chan, HP; Lai, TL
• 署名单位: National University of Singapore; Stanford University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2000
• 页码: 1638-1669
• 关键词: likelihood ratio tests; large deviations; limit-theorem; tubes; volume; statistics; regression; inference; number

摘要

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 provide 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.