High Dimensional Spatial Rank Test for Two-Sample Location Problem

Abstract

This article concerns tests for the two-sample location problem when the dimension is larger than the sample size. The traditional multivariate-rank-based procedures cannot be used in high dimensional settings because the sample scatter matrix is not available. We propose a novel high-dimensional spatial rank test in this article. The asymptotic normality is established. We can allow the dimension being almost the exponential rate of the sample sizes. Simulations demonstrate that it is very robust and efficient in a wide range of distributions.