Generalized Nonparametric Composite Tests for High-Dimensional Data

In this paper, composite high-dimensional nonparametric tests for two samples are proposed, by using component-wise Wilcoxon-Mann-Whitney-type statistics. No distributional assumption, moment condition, or parametric model is required for the development of the tests and the theoretical results. Two approaches are employed, for estimating the asymptotic variance of the composite statistic, leading to two tests. In both cases, banding of the covariance matrix to estimate variance of the test statistic is involved. An adaptive algorithm, for selecting the banding window width, is proposed. Numerical studies are provided, to show the favorable performance of the new tests in finite samples and under varying degrees of dependence.