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

Author:

Schäfer Juliane,Strimmer Korbinian

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.

Publisher

Walter de Gruyter GmbH

Subject

Computational Mathematics,Genetics,Molecular Biology,Statistics and Probability

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