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

Author

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  • Schäfer Juliane

    (Department of Statistics, University of Munich, Germany)

  • Strimmer Korbinian

    (Department of Statistics, University of Munich, Germany)

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.

Suggested Citation

  • Schäfer Juliane & Strimmer Korbinian, 2005. "A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-32, November.
    • Handle: RePEc:bpj:sagmbi:v:4:y:2005:i:1:n:32
    DOI: 10.2202/1544-6115.1175
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