Constrained estimation and some useful results in several multivariate models

In this paper, we are interested in an estimation problem concerning the regression coefficient parameter matrices of M independent multivariate multiple linear models. More specifically, we consider the case where the M parameter matrices are suspected of satisfying some restrictions. Given such uncertainty, we study a class of shrinkage estimators which give an improvement over the performance of the quasi-maximum likelihood estimator (QMLE). To this end, we derive a theorem which is useful in establishing the asymptotic distributional risk function of a class of shrinkage estimators of the regression coefficient parameter matrices.