Open Access
September 2017 Testing high-dimensional covariance matrices, with application to detecting schizophrenia risk genes
Lingxue Zhu, Jing Lei, Bernie Devlin, Kathryn Roeder
Ann. Appl. Stat. 11(3): 1810-1831 (September 2017). DOI: 10.1214/17-AOAS1062


Scientists routinely compare gene expression levels in cases versus controls in part to determine genes associated with a disease. Similarly, detecting case-control differences in co-expression among genes can be critical to understanding complex human diseases; however, statistical methods have been limited by the high-dimensional nature of this problem. In this paper, we construct a sparse-Leading-Eigenvalue-Driven (sLED) test for comparing two high-dimensional covariance matrices. By focusing on the spectrum of the differential matrix, sLED provides a novel perspective that accommodates what we assume to be common, namely sparse and weak signals in gene expression data, and it is closely related with sparse principal component analysis. We prove that sLED achieves full power asymptotically under mild assumptions, and simulation studies verify that it outperforms other existing procedures under many biologically plausible scenarios. Applying sLED to the largest gene-expression dataset obtained from post-mortem brain tissue from Schizophrenia patients and controls, we provide a novel list of genes implicated in Schizophrenia and reveal intriguing patterns in gene co-expression change for Schizophrenia subjects. We also illustrate that sLED can be generalized to compare other gene-gene “relationship” matrices that are of practical interest, such as the weighted adjacency matrices.


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Lingxue Zhu. Jing Lei. Bernie Devlin. Kathryn Roeder. "Testing high-dimensional covariance matrices, with application to detecting schizophrenia risk genes." Ann. Appl. Stat. 11 (3) 1810 - 1831, September 2017.


Received: 1 November 2016; Revised: 1 April 2017; Published: September 2017
First available in Project Euclid: 5 October 2017

zbMATH: 1380.62262
MathSciNet: MR3709579
Digital Object Identifier: 10.1214/17-AOAS1062

Keywords: Covariance matrix , High-dimensional data , Permutation test , sparse principal component analysis

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.11 • No. 3 • September 2017
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