Reduced-rank estimation of the difference between two covariance matrices

We consider in m x m covariance matrices, Sigma(1) and Sigma(2), which satisfy Sigma(2) - Sigma(1) = Delta, where Delta has a specified rank. Maximum likelihood estimators of Sigma(1), and Sigma(2) are obtained when sample covariance matrices having Wishart distributions are available and rank(Delta) is known. The likelihood ratio statistic for a test about the value of rank(Delta) is also given and some properties of its null distribution are obtained. The methods developed in this paper are illustrated through an example. (C) 2009 Elsevier B.V. All rights reserved.