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.
%0 Journal Article
%1 citeulike:1485976
%A Schäfer, Juliane
%A Strimmer, Korbinian
%C Department of Statistics, University of Munich, Germany. schaefer@stat.math.ethz.ch
%D 2005
%J Statistical Applications in Genetics and Molecular Biology
%K statistics
%N 1
%R 10.2202/1544-6115.1175
%T A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics
%U http://www.uni-leipzig.de/\~strimmer/lab/publications/journals/shrinkcov2005.pdf
%V 4
%X 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.
@article{citeulike:1485976,
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.}},
added-at = {2019-06-18T20:47:03.000+0200},
address = {Department of Statistics, University of Munich, Germany. schaefer@stat.math.ethz.ch},
author = {Sch\"{a}fer, Juliane and Strimmer, Korbinian},
biburl = {https://www.bibsonomy.org/bibtex/2f188475e926436d55b3c785dde07abc4/alexv},
citeulike-article-id = {1485976},
citeulike-linkout-0 = {http://www.uni-leipzig.de/\~{}strimmer/lab/publications/journals/shrinkcov2005.pdf},
citeulike-linkout-1 = {http://dx.doi.org/10.2202/1544-6115.1175},
citeulike-linkout-2 = {http://view.ncbi.nlm.nih.gov/pubmed/16646851},
citeulike-linkout-3 = {http://www.hubmed.org/display.cgi?uids=16646851},
day = 14,
doi = {10.2202/1544-6115.1175},
interhash = {88dcbb43d8278288a1863fd1068a3ed4},
intrahash = {f188475e926436d55b3c785dde07abc4},
issn = {1544-6115},
journal = {Statistical Applications in Genetics and Molecular Biology},
keywords = {statistics},
month = jan,
number = 1,
pmid = {16646851},
posted-at = {2011-09-16 23:09:56},
priority = {2},
timestamp = {2019-06-18T20:47:03.000+0200},
title = {{A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics}},
url = {http://www.uni-leipzig.de/\~{}strimmer/lab/publications/journals/shrinkcov2005.pdf},
volume = 4,
year = 2005
}