Comparing Large Covariance Matrices under Weak Conditions on the Dependence Structure and Its Application to Gene Clustering

Comparing Large Covariance Matrices under Weak Conditions on the Dependence Structure and Its Application to Gene Clustering

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...

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Bibliographic Details
Published in:Biometrics 2017-03, Vol.73 (1), p.31-41
Main Authors: Chang, Jinyuan, Zhou, Wen, Zhou, Wen-Xin, Wang, Lan
Format: Article
Language:eng ; fre
Subjects:
Algorithms
Analysis of Variance
Asthma
Asthma - genetics
BIOMETRIC METHODOLOGY
Cluster Analysis
Clustering
Computer Simulation
Covariance matrix
Data Interpretation, Statistical
Data processing
Dependence
Differential expression analysis
Disease control
Fourier analysis
Gene clustering
Gene expression
Gene Expression Profiling
Genes
Genomics
Genomics - methods
Genomics - statistics & numerical data
High dimension
Humans
Hypothesis testing
Parametric bootstrap
Sample Size
Sparsity
Online Access:Get full text
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Summary: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.
ISSN:0006-341X
1541-0420