title: A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics.
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.
authors.affiliation: Department of Statistics, University of Munich, Germany. schaefer@stat.math.ethz.ch
authors.forename: Juliane
authors.initials: J
authors.lastname: Schäfer
authors.forename: Korbinian
authors.initials: K
authors.lastname: Strimmer