Simultaneously Testing for Location and Scale Parameters of Two Multivariate Distributions

Abstract

In this article, we propose nonparametric tests for simultaneously testing equality of location and scale parameters of two multivariate distributions by using nonparametric combination theory. Our approach is to combine the data depth based location and scale tests using combining function to construct a new data depth based test for testing both location and scale parameters. Based on this approach, we have proposed several tests. Fisher's permutation principle is used to obtain p-values of the proposed tests. Performance of proposed tests has been evaluated in terms of empirical power for symmetric and skewed multivariate distributions and compared to the existing test based on data depth. The proposed tests are also applied to a real-life data set for illustrative purpose.