Permutation tests of multivariate location using data depth

Abstract

We provide two classes of affine invariant statistics based on data depth to test the equality of mean vectors in multivariate paired data. The proposed tests are defined based on the depth values of the deepest point of the sample relative to the negative of the multivariate sample and the expected median under the null hypothesis. The tests are implemented through the idea of the permutation procedure. No distributional assumption is imposed on the data, except that the permutation test assumes a centrally symmetric distribution of the paired data. A simulation study compares the new tests to some competitors. The results show that the new tests are highly competitive for a wide variety of distributional models. More specifically, the results show that the tests based on the halfspace, simplicial, and projection depth functions perform well compared to other methods and are the most robust. A real data example illustrating the use of the tests is also presented.