EQUIVARIANT ESTIMATION OF A NORMAL-MEAN VECTOR USING A NORMAL CONCOMITANT VECTOR FOR COVARIANCE ADJUSTMENT

Equivariant estimators of the first p components of a (p + q)-variate normal mean vector are considered when the remaining q components of the mean vector are known. Using a natural group of affine transformations these equivariant estimators are characterized. A detailed comparison in terms of risk functions with respect to a normalized quadratic loss function is provided for a specific subclass of equivariant estimators.