Robust elementwise estimation of a dispersion matrix

Most of the existing robust methods for estimating a covariance or correlation matrix involve a multivariate approach in which matrix elements are estimated via simultaneous manipulation of all variables. These methods are generally based on complex iterative algorithms and hence are rather difficult to implement. The purpose of this article is to recommend an easy to implement noniterative robust method for estimating a dispersion matrix, based on an elementwise estimation approach. Simple expressions are provided for robust estimators of variances and covariances based, in part, on a modified A-estimator of scale discussed previously by Lax (1985, Journal of the American Statistical Association 80, 736-741). A Monte Carlo study is used to compare the performance of the proposed noniterative method with that of some iterative procedures studied in the literature. A numerical example involving robust estimation of variance components is presented as an application of the proposed methodology.