A high-dimensional inverse norm sign test for two-sample location problems

Abstract

In this article, we focus on the two-sample location testing problem for high-dimensional data, where the data dimension is potentially much larger than the sample sizes. First, we construct a general class of weighted spatial sign tests for the two-sample location problem, which can include some existing high-dimensional nonparametric tests. Then, in this article, we find a locally most powerful test by choosing the inverse norm weight function, named the two-sample inverse norm sign test (tINST). The proposed test can be viewed as an extension of the inverse norm sign test devised for the one-sample problem. We establish the asymptotic properties of the proposed test, which indicate that it is consistent and has greater power than competing tests that belong to the proposed class of weighted spatial sign tests for two-sample location problems. Finally, a large number of numerical investigations and a practical biomedical example demonstrate the power and robustness advantages of the proposed test.