A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics

Schäfer Juliane and Strimmer Korbinian
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Schäfer Juliane: Department of Statistics, University of Munich, Germany
Strimmer Korbinian: Department of Statistics, University of Munich, Germany

Statistical Applications in Genetics and Molecular Biology, 2005, vol. 4, issue 1, 32

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.

Keywords: Shrinkage; covariance estimation; “small n; large p” problem; graphical Gaussian model (GGM); genetic network; gene expression. (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (152)

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DOI: 10.2202/1544-6115.1175

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