A note on necessary and sufficient conditions of existence and uniqueness for the maximum likelihood estimator of a Kronecker-product variance–covariance matrix

Abstract

In this note, the author discusses the problem of maximum likelihood (ML) estimation for the Kronecker product of two positive definite variance–covariance matrices, with focus on necessary and sufficient conditions of existence and uniqueness for the ML estimator. Recent and earlier references, from the author and others, are scrutinized. The discussion includes computational aspects, as an estimation algorithm is used in the absence of analytical solutions. A timely update is provided as a result.