2014/06/30 by Jinyuan Chang, Chao Zheng, Wen-Xin Zhou +1 · 51 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · #Clustering high-dimensional data #Covariance #False discovery rate #Feature (linguistics) #Gene expression and cancer classification #High dimensional #Multiple comparisons problem #Parametric statistics #Random Matrices and Applications #Statistical Methods and Inference #Statistical hypothesis testing #math.ST #stat.ME #stat.TH
paper · pdf · doi:10.1111/biom.12695
published in Biometrics 73(4), 1300-1310 (Oxford University Press) · 34 pages, 10 figures; Accepted for biometrics
arxiv created 2017/02/24 · openalex publication_date 2017/03/31 · arxiv updated 2018/01/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.