A double sequential weighted probability ratio test for one-sided composite hypotheses

For sequential test plans, we propose the weighted expected sample size (WESS) to evaluate the overall performance on the parameter interval of interest. Based on minimizing the WESS to control the expected sample sizes, we develop the method of double sequential weighted probability ratio test (2-SWPRT) for one-sided composite hypotheses. It is proved that the 2-SWPRT has a finite stopping time and is the asymptotically optimal test. Simulation studies show that the 2-SWPRT not only has the smallest WESS compared with the SPRT and 2-SPRT, but also is superior to the 2-SPRT and comparable with the SPRT under the null and alternative hypotheses. Moreover, the relative mean index (RMI) also shows the 2-SWPRT is an efficient method to improve the overall performance.