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Mathematical Problems in Engineering
Volume 2015, Article ID 356587, 8 pages
Research Article

Asymptotic Optimality of Combined Double Sequential Weighted Probability Ratio Test for Three Composite Hypotheses

School of Finance and Statistics, East China Normal University, Shanghai 200241, China

Received 24 December 2014; Revised 13 March 2015; Accepted 15 March 2015

Academic Editor: Antonino Laudani

Copyright © 2015 Lei Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose the weighted expected sample size (WESS) to evaluate the overall performance on the indifference-zones for three composite hypotheses’ testing problem. Based on minimizing the WESS to control the expected sample sizes, a new sequential test is developed by utilizing two double sequential weighted probability ratio tests (2-SWPRTs) simultaneously. It is proven that the proposed test has a finite stopping time and is asymptotically optimal in the sense of asymptotically minimizing not only the expected sample size but also any positive moment of the stopping time on the indifference-zones under some mild conditions. Simulation studies illustrate that the proposed test has the smallest WESS and relative mean index (RMI) compared with Sobel-Wald and Whitehead-Brunier tests.