Empirical Bayes Estimation of the Multivariate Normal Covariance Matrix

Abstract

Let Sp×p have a Wishart distribution with scale matrix Σ and k degrees of freedom. Estimators of Σ are given for each of the loss functions L1(Σ^,Σ)=tr(Σ^Σ−1)−logdet(Σ^Σ−1)−p and L2(Σ^,Σ)=tr(Σ^Σ−1−I)2. The obvious estimators of Σ are the scalar multiples of S, i.e., aS where 0