On a Conjecture of Krishnamoorthy and Gupta,
AbstractWe 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Multivariate Analysis.
Volume (Year): 62 (1997)
Issue (Month): 1 (July)
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Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description
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