TY - JOUR
T1 - Estimation of a covariance matrix with zeros
AU - Chaudhuri, Sanjay
AU - Drton, Mathias
AU - Richardson, Thomas S.
N1 - Funding Information:
ACKNOWLEDGEMENT We thank Steffen Lauritzen for pointing out the duality between iterative conditional and iterative proportional fitting, and Art Owen for suggesting use of empirical likelihood. Sanjay Chaudhuri thanks Mark Handcock for helpful discussions. We also thank the editor and two anonymous referees for comments leading to improved presentation of the paper. This work was supported by grants from the U.S. National Science Foundation, the U.S. National Institutes of Health, the University of Washington Royalty Research Fund, the William and Flora Hewlett Foundation, the U.S. National Institute of Child Health and Human Development and the National University of Singapore.
PY - 2007/3
Y1 - 2007/3
N2 - We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call iterative conditional fitting, for computing the maximum likelihood estimate of the constrained covariance matrix, under the assumption of multivariate normality. In contrast to previous approaches, this algorithm has guaranteed convergence properties. Dropping the assumption of multivariate normality, we show how to estimate the covariance matrix in an empirical likelihood approach. These approaches are then compared via simulation and on an example of gene expression.
AB - We consider estimation of the covariance matrix of a multivariate random vector under the constraint that certain covariances are zero. We first present an algorithm, which we call iterative conditional fitting, for computing the maximum likelihood estimate of the constrained covariance matrix, under the assumption of multivariate normality. In contrast to previous approaches, this algorithm has guaranteed convergence properties. Dropping the assumption of multivariate normality, we show how to estimate the covariance matrix in an empirical likelihood approach. These approaches are then compared via simulation and on an example of gene expression.
KW - Covariance graph
KW - Empirical likelihood
KW - Graphical model
KW - Marginal independence
KW - Maximum likelihood estimation
KW - Multivariate normal distribution
UR - http://www.scopus.com/inward/record.url?scp=33947153898&partnerID=8YFLogxK
U2 - 10.1093/biomet/asm007
DO - 10.1093/biomet/asm007
M3 - Article
AN - SCOPUS:33947153898
SN - 0006-3444
VL - 94
SP - 199
EP - 216
JO - Biometrika
JF - Biometrika
IS - 1
ER -