Abstract: | Let Sp × p have a Wishart distribution with parameter matrix Σ and n degrees of freedom. We consider here the problem of estimating the precision matrix Σ?1 under the loss functions L1(σ) tr (σ) - log |σ| and L2(σ) = tr (σ). James-Stein-type estimators have been derived for an arbitrary p. We also obtain an orthogonal invariant and a diagonal invariant minimax estimator under both loss functions. A Monte-Carlo simulation study indicates that the risk improvement of the orthogonal invariant estimators over the James-Stein type estimators, the Haff (1979) estimator, and the “testimator” given by Sinha and Ghosh (1987) is substantial. |