Minimax estimators of a covariance matrix

AbstractLet S: p × p have a nonsingular Wishart distribution with unknown matrix Σ and n degrees of freedom, n ≥ p. For estimating Σ, a family of minimax estimators, with respect to the entropy loss, is presented. These estimators are of the form ∑(S) = RΦ(L) Rt, where R is orthogonal, L and Φ are diagonal, and RLRt = S. Conditions under which the components of Φ and L follow the same order relation are stated (i.e., writing L = diag((l1, …, lp)t) and Φ = diag((ϕ1, …, ϕp)t) it is true that ϕ1 ≥ … ≥ ϕp if and only if l1 ≥ … ≥ lp). Simulation results are included