title: Simulation-based hypothesis testing of high dimensional means under covariance heterogeneity.
abstract: In this article, we study the problem of testing the mean vectors of high dimensional data in both one-sample and two-sample cases. The proposed testing procedures employ maximum-type statistics and the parametric bootstrap techniques to compute the critical values. Different from the existing tests that heavily rely on the structural conditions on the unknown covariance matrices, the proposed tests allow general covariance structures of the data and therefore enjoy wide scope of applicability in practice. To enhance powers of the tests against sparse alternatives, we further propose two-step procedures with a preliminary feature screening step. Theoretical properties of the proposed tests are investigated. Through extensive numerical experiments on synthetic data sets and an human acute lymphoblastic leukemia gene expression data set, we illustrate the performance of the new tests and how they may provide assistance on detecting disease-associated gene-sets. The proposed methods have been implemented in an R-package HDtest and are available on CRAN.
authors.affiliation: School of Statistics, Southwestern University of Finance and Economics, Chengdu, Sichuan 611130, China.
authors.forename: Jinyuan
authors.initials: J
authors.lastname: Chang
authors.affiliation: School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia.
authors.forename: Chao
authors.initials: C
authors.lastname: Zheng
authors.affiliation: Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08544, U.S.A.
authors.forename: Wen-Xin
authors.initials: WX
authors.lastname: Zhou
authors.affiliation: Department of Statistics, Colorado State University, Fort Collins, Colorado 80523, U.S.A.
authors.forename: Wen
authors.initials: W
authors.lastname: Zhou
mesh_terms: D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D015870:Gene Expression; D056726:Genetic Association Studies / Q000706:statistics & numerical data; D006801:Humans; D054198:Precursor Cell Lymphoblastic Leukemia-Lymphoma / Q000235:genetics
keywords: Feature screening; High dimension; Hypothesis testing; Normal approximation; Parametric bootstrap; Sparsity