Asymptotic optimality of double sequential mixture likelihood ratio test

Abstract

In this article, we propose to use the weighted expected sample size (WESS) to evaluate the overall performance of sequential test plans on a finite set of parameters. Motivated by minimizing the WESS to control the expected sample sizes, we develop the method of double sequential mixture likelihood ratio test (2-SMLRT) for one-sided composite hypotheses. It is proved that the 2-SMLRT is asymptotically optimal on and its stopping time is finite under some conditions. The 2-SMLRT is general and includes the sequential probability ratio test (SPRT) and the double sequential probability ratio test (2-SPRT) as special cases. Simulation studies show that compared with the SPRT and 2-SPRT, the 2-SMLRT has smaller WESS and relative mean index with less or comparable expected sample sizes when the null hypothesis or alternative hypothesis holds.

Keywords:

• SPRT
• 2-SPRT
• mixture likelihood ratio
• asymptotically optimal
• finite stopping time

AMS Subject Classifications::

• 62L10
• 62P10
• 62P30

Acknowledgements

This research was supported by grants from the National Natural Science Foundation of China (11101156, 11271135, 11001083) and the Fundamental Research Funds for the Central Universities.