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

作者：Wang, Lei^*; Pu, Xiaolong; Li, Yan

来源：Mathematical Problems in Engineering, 2015, 2015: UNSP 356587.

DOI：10.1155/2015/356587

• Asymptotic optimality
• Asymptotically optimal
• Composite hypothesis
• Indifference zone
• Sequential tests
• Simulation studies
• Stopping time
• Weighted probability

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.

• 出版日期2015
• 单位华东师范大学