AbstractLetSp ×phave a Wishart distribution with parameter matrix Σ andndegrees of freedom. We consider here the problem of estimating the precision matrix Σ−1under the loss functionsL1(σ) tr (σ) ‐ log |σ| andL2(σ) = tr (σ). James‐Stein‐type estimators have been derived for an arbitraryp. 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 Ghos