Neyman’s truncation test for two-sample means under high dimensional setting

Abstract

Multivariate two-sample testing problems often arise from the statistical analysis for scientific data, especially for bioinformatics data. To detect components with different values between two mean vectors, well-known procedures are to apply Sum-of-Squares type tests, such as Hotelling’s ${\mathit{T}}^2$-test. However, such a test is not suitable to high dimensional settings because of singular covariance matrix and accumulated errors. Nowadays, a lot of test methods for high dimensional data are developed, mainly including two types, Sum-of-Squares type and Max type. The Sum-of-Squares type test statistics have poor performance against sparse alternatives. And the Max type test statistic is not powerful enough to deal with non-sparse datasets. In this paper, we propose a Max-Partial-Sum type statistic named Neyman’s Truncation test, which is conducted by maximum partial sums of marginal test statistics. Besides non-sparse datasets, Neyman’s Truncation test also has great power against dense and sparse alternatives. The asymptotic distribution of the test statistic under null hypothesis is obtained and the power of the test is analyzed. To avoid the slow convergence rate of the asymptotic distribution, we realize our method by Bootstrap procedures. Simulation studies and the analysis of leukemia dataset are carried out to verify the numerical performance.