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On a Conjecture of Krishnamoorthy and Gupta

✍ Scribed by François Perron

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
325 KB
Volume
62
Category
Article
ISSN
0047-259X

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✦ Synopsis

We consider the problem of estimating the precision matrix (7 &1 ) under a fully invariant convex loss. Suppose that there exists a minimax constant risk estimator 8 (say) for this problem. K. Krishnamoorthy and A. K. Gupta have proposed an operation which transforms this estimator into an orthogonally invariant estimator 8* (say) and they have a conjecture saying that 8* 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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