Reduced-rank linear regression

This paper considers the problem of maximum likelihood (ML) estimation for reduced-rank linear regression equations with noise of arbitrary covariance. An explicit expression for the ML estimate of the regression matrix is derived. A generalized likelihood ratio (GLRT) test as also proposed, for estimating the rank of the regression matrix. Computer simulations and numerical examples indicate the superiority of the proposed estimator, as compared to a traditional least-squares approach that does not exploit the reduced rank property in an optimal way