title: Comparing large covariance matrices under weak conditions on the dependence structure and its application to gene clustering.
abstract: Comparing large covariance matrices has important applications in modern genomics, where scientists are often interested in understanding whether relationships (e.g., dependencies or co-regulations) among a large number of genes vary between different biological states. We propose a computationally fast procedure for testing the equality of two large covariance matrices when the dimensions of the covariance matrices are much larger than the sample sizes. A distinguishing feature of the new procedure is that it imposes no structural assumptions on the unknown covariance matrices. Hence, the test is robust with respect to various complex dependence structures that frequently arise in genomics. We prove that the proposed procedure is asymptotically valid under weak moment conditions. As an interesting application, we derive a new gene clustering algorithm which shares the same nice property of avoiding restrictive structural assumptions for high-dimensional genomics data. Using an asthma gene expression dataset, we illustrate how the new test helps compare the covariance matrices of the genes across different gene sets/pathways between the disease group and the control group, and how the gene clustering algorithm provides new insights on the way gene clustering patterns differ between the two groups. 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.|School of Mathematics and Statistics, University of Melbourne, Parkville, Victoria 3010, Australia.
authors.forename: Jinyuan
authors.initials: J
authors.lastname: Chang
authors.affiliation: Department of Statistics, Colorado State University, Fort Collins, Colorado 80523, U.S.A.
authors.forename: Wen
authors.initials: W
authors.lastname: Zhou
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: School of Statistics, University of Minnesota, Minneapolis, Minnesota 55455, U.S.A.
authors.forename: Lan
authors.initials: L
authors.lastname: Wang
mesh_terms: D000465:Algorithms; D000704:Analysis of Variance; D001249:Asthma / Q000235:genetics; D016000:Cluster Analysis; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D020869:Gene Expression Profiling; D023281:Genomics / Q000379:methods* / Q000706:statistics & numerical data; D006801:Humans; D018401:Sample Size
keywords: Differential expression analysis; Gene clustering; High dimension; Hypothesis testing; Parametric bootstrap; Sparsity