A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics

Statistical Applications in Genetics and Molecular Biology
Juliane Schäfer, Korbinian Strimmer

Abstract

Inferring large-scale covariance matrices from sparse genomic data is an ubiquitous problem in bioinformatics. Clearly, the widely used standard covariance and correlation estimators are ill-suited for this purpose. As statistically efficient and computationally fast alternative we propose a novel shrinkage covariance estimator that exploits the Ledoit-Wolf (2003) lemma for analytic calculation of the optimal shrinkage intensity. Subsequently, we apply this improved covariance estimator (which has guaranteed minimum mean squared error, is well-conditioned, and is always positive definite even for small sample sizes) to the problem of inferring large-scale gene association networks. We show that it performs very favorably compared to competing approaches both in simulations as well as in application to real expression data.

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Citations

Nov 19, 2009·TAG. Theoretical and applied genetics. Theoretische und angewandte Genetik·Sandra AndorfDirk Repsilber
Nov 1, 2012·IIE Transactions : Industrial Engineering Research & Development·Shuai HuangLi Yao
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Nov 26, 2009·BMC Bioinformatics·Nicole KrämerAnne-Laure Boulesteix
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Oct 19, 2010·BMC Bioinformatics·Isabel A Nepomuceno-ChamorroJose C Riquelme
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