Construction of Improved Estimators for the Regression Coefficient Matrix in GMANOVA Model

This paper extensively investigates the theory of estimating the regression coefficient matrix for the normal GNANOVA model. We explicitly construct estimators which improve the maximum likehood estimator under an invariant scalar loss function. These include the double shrinkage estimators and those shirinking the maximum likelihood estimators diretly. The underlying method is the decomposition of the problem into the conditional subproblems due to Kariya and Konnno(1994)and application of integration-by part techiniqe to derive an unbiased estimate of the risk for certain class of invariant estimators.