Abstract

We present a class of Shrinkage-type estimators for the mean matrix of scale mixtures of multivariate normal distributions with an unknown covariance structure. The established results generalize the existing methods in literature in four ways. First, we consider a parametric estimation problem that encompasses the classical vector setting as a special case. Second, we relax distributional assumptions, allowing for a substantially broader class of sampling distributions, including singular and degenerate cases. Third, we introduce a new class of Shrinkage matrix estimators and establish necessary and sufficient conditions for the finiteness of their risk functions. Fourth, under a general loss function, we derive sufficient conditions under which these estimators dominate the classical maximum likelihood estimator. In addition, our theoretical results are applicable to a broad range of statistical methods and can be applied to both classical low-dimensional and high-dimensional datasets.