Estimation of the Multivariate Normal Precision Matrix under the Entropy Loss

Let X₁, , X_n (n > p) be a random sample from multivariate normal distribution N_p(, ), where R^p and is a positive definite matrix, both and being unknown. We consider the problem of estimating the precision matrix ^–1. In this paper it is shown that for the entropy loss, the best lower-triangular affine equivariant minimax estimator of ^–1 is inadmissible and an improved estimator is explicitly constructed. Note that our improved estimator is obtained from the class of lower-triangular scale equivariant estimators.