ROBUST ELEMENTWISE ESTIMATION OF A DISPERSION MATRIX

Most of the existing robust methods for estimating a covariance or cor relation matrix involve a multivariate approach in which matrix elemen ts 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 estimati ng a dispersion matrix, based on an elementwise estimation approach. S imple expressions are provided for robust estimators of variances and covariances based, in part, on a modified A-estimator of scale discuss ed previously by Lax (1985, Journal of the American Statistical Associ ation 80, 736-741). A Monte Carlo study is used to compare the perform ance of the proposed noniterative method with that of some iterative p rocedures studied in the literature. A numerical example involving rob ust estimation of variance components is presented as an application o f the proposed methodology.