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

Abstract

a b s t r a c tThis 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.

On eigenvalues of a high-dimensional spatial-sign covariance matrix

“…Recent works related to the high-dimensional SSCM B n (or its variants) include Zou et al (2014), Feng and Sun (2016), Li et al (2016) and Chakraborty and Chaudhuri (2017). A common feature in these papers is that given a specific null hypothesis on the population location or scatter, under elliptical distributions, in a one-sample or two-sample design, the authors have in their disposal a specific test statistic which is an explicit function of B n (or its variants).…”