  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.
