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

作者：Juliane Schäfer, Korbinian Strimmer · 发表于：Statistical Applications in Genetics and Molecular Biology · 年份：2005 · DOI：10.2202/1544-6115.1175 · 被引用次数：1627 · 研究领域：Gene expression and cancer classification、Bioinformatics and Genomic Networks、Genetic Mapping and Diversity in Plants and Animals

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.