A robust testing procedure for the equality of covariance matrices

In classical statistics the likelihood ratio statistic used in testing hypotheses about covariance matrices does not have a closed form distribution, but asymptotically under strong normality assumptions is a function of the chi(2)-distribution. This distributional approximation totally fails if the normality assumption is not completely met. In this paper we will present multivariate robust testing procedures for the scatter matrix Sigma using S-estimates. We modify the classical likelihood ratio test (LRT) into a robust LRT by substituting the robust estimates in the formula in place of classical estimates. A nonlinear formula is also suggested to approximate the degrees of freedom for the approximated Wishart distribution proposed for S-estimates of the shape matrix Sigma. We present simulation results to compare the validity and the efficiency of the robust likelihood test to the classical likelihood test. (c) 2004 Elsevier B.V. All rights reserved.