On a Conjecture of Krishnamoorthy and Gupta,
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.
Volume (Year): 62 (1997)
Issue (Month): 1 (July)
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- Loh, Wei-Liem, 1991. "Estimating covariance matrices II," Journal of Multivariate Analysis, Elsevier, vol. 36(2), pages 163-174, February.
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