The limiting distribution of combining the t and Wilcoxon rank sum tests

In two-sample testing problems, Student'st-test and the Wilcoxon rank-sum test are often used to test the location parameter, and have been discussed by many authors over the years. The Wilcoxon rank-sum test is more powerful than thet-test for non-normal data. Previous studies consider combining these two tests within a maximum test and show that it controls the type I error and has good statistical power for various distributions. The power of the maximum test is similar to the more powerful of the two tests. However, the limiting distribution of the test has not been derived. This study derives the limiting distribution of the maximum test under the null hypothesis and uses simulations to investigate the convergence of the maximum test to the limiting distribution in various cases.