On a conjecture of Krishnamoorthy and Gupta

[摘要] We consider the problem of estimating the precision matrix (Sigma-1) under a fully invariant convex loss. Suppose that there exists a minimax constant risk estimator Phi (say) for this problem. K. Krishnamoorthy and A. K. Gupta have proposed an operation which transforms this estimator into an orthogonally invariant estimator Phi* (say) and they have a conjecture saying that Phi* is minimax as well. This paper contains two parts. In the first part, we present counterexamples. In the second part, we elaborate a technique which can be used to prove that certain estimators are minimax. This technique is then applied successfully to some of the estimators proposed in the Krishnamoorthy and Gupta paper. (C) 1997 Academic Press.

[发布日期] 1997-07-01

[关键词] covariance matrix;precision matrix;equivariant estimators;unbiased estimate of the risk;Wishart distribution;Haar probability measure on the orthogonal group