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Statistical Applications in Genetics and Molecular Biology

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Volume 4, Issue 1 (Nov 2005)


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

Juliane Schäfer
  • Department of Statistics, University of Munich, Germany
/ Korbinian Strimmer
  • Department of Statistics, University of Munich, Germany
Published Online: 2005-11-14 | DOI: https://doi.org/10.2202/1544-6115.1175

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.

About the article

Published Online: 2005-11-14

Citation Information: Statistical Applications in Genetics and Molecular Biology, ISSN (Online) 1544-6115, ISSN (Print) 2194-6302, DOI: https://doi.org/10.2202/1544-6115.1175. Export Citation

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