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Biometrika Advance Access published online on February 12, 2007
Biometrika, doi:10.1093/biomet/asm007
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Copyright © Biometrika Trust

Estimation of a covariance matrix with zerosEstimation of a covariance matrix

Sanjay Chaudhuri, Mathias Drton and Thomas S. Richardson

Department of Statistics and Applied Probability, Faculty of Science, 6 Science Drive 2, National University of Singapore, 117546, Singapore
Department of Statistics, The University of Chicago, 5734 S. University Avenue, Chicago, Illinois 60637, U.S.A.
Department of Statistics, University of Washington, Box 354322, Seattle, Washington 98105-4322, U.S.A.

sanjay{at}stat.nus.edu.sg

drton{at}galton.uchicago.edu

tsr{at}stat.washington.edu

Received for publication 1 August 2005. Revision received 1 June 2006.
  Abstract

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.

Key Words: Covariance graph • Empirical likelihood • Graphical model • Marginal independence • Maximum likelihood estimation • Multivariate normal distribution


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