Title: The multivariate statistic based on combining the t test and Wilcoxon test
Authors: Masato Kitani - Tokyo University of Science (Japan) [presenting]
Hidetoshi Murakami - Tokyo University of Science (Japan)
Abstract: A multivariate two-sample testing problem is one of the most important topics in nonparametric statistics. The multivariate nonparametric tests based on the Jureckova-Kalina ranks of distance have been discussed. For univariate case, it is proposed that a maximum test combining the t test and Wilcoxon's rank-sum test. It was shown that the maximum test has a good power for a variety of distributions, and its power is close to that of more powerful of the two tests. We obtain the null distribution of maximum test and extend the maximum test for the multivariate observation by using the Jureckova-Kalina ranks of distances. Simulations are used to investigate the power of suggested test for the two-sided alternative with various distributions. The behavior of proposed test is compared with the Hotelling's $T^2$ test. The results show that the proposed test statistic is more suitable than various existing statistics for testing a shift in the location and location-scale parameters.