Estimation of a Covariance Matrix with Zeros

Details Estimation of a Covariance Matrix with Zeros Estimation of a Covariance Matrix with Zeros

2005-08-15

arxiv.org/abs/math/0508268v1

Biometrika 2007, Vol. 94, No. 1, 199-216

Mathematics

Statistics Theory

25 pages

Scientific paper

10.1093/biomet/asm007

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 estimator 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.

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