New nonparametric tests based on data depth for multivariate multi-sample location problem

Abstract

Data depth based nonparametric tests for multivariate multisample location problem are provided which extend the depth based nonparametric test for multivariate two-sample location problem by Shirke and Khorate (2018) [Shirke, D.T. and Khorate, S.D., 2018. Two-sample nonparametric test for testing equality of locations based on data depth. Journal of the Indian Society for Probability and Statistics, 19, pp. 9-23.] to the multi-sample setting. Proposed tests are based on the correlations among the depths of data points. Power comparison of proposed tests with the existing depth based nonparametric tests is provided using a simulation study based on a permutation test. Simulation study reveals that the proposed tests give comparable powers compared to the existing data depth based nonparametric tests. Proposed tests are illustrated with real life data sets.