A simpler spatial-sign-based two-sample test for high-dimensional data

This article concerns the tests for the equality of two location parameters when the data dimension is larger than the sample size. Existing spatial-sign-based procedures are not robust with respect to high dimensionality, producing tests with the type-I error rates that are much larger than the nominal levels. We develop a correction that makes the sign-based tests applicable for high-dimensional data, allowing the dimensionality to increase as the square of the sample size. We show that the proposed test statistic is asymptotically normal under elliptical distributions and demonstrate that it has good size and power in a wide range of settings by simulation.