Nearly Minimax One-Sided Mixture-Based Sequential Tests

作者：Fellouris Georgios; Tartakovsky Alexander G^*

来源：Sequential Analysis, 2012, 31(3): 297-325.

DOI：10.1080/07474946.2012.694346

• Asymptotic optimality
• Minimax tests
• Mixtures rules
• One-sided sequential tests
• Open-ended tests
• Power one tests

We focus on one-sided, mixture-based stopping rules for the problem of sequential testing a simple null hypothesis against a composite alternative. For the latter, we consider two cases-either a discrete alternative or a continuous alternative that can be embedded into an exponential family. For each case, we find a mixture-based stopping rule that is nearly minimax in the sense of minimizing the maximal Kullback-Leibler information. The proof of this result is based on finding an almost Bayes rule for an appropriate sequential decision problem and on high-order asymptotic approximations for the performance characteristics of arbitrary mixture-based stopping times. We also evaluate the asymptotic performance loss of certain intuitive mixture rules and verify the accuracy of our asymptotic approximations with simulation experiments.

• 出版日期2012