On minimaxity of the normal precision matrix estimator of Krishnamoorthy and Gupta

We consider the orthogonally invariant estimation problem of the inverse of the scale matrix of Wishart distribution using Stein's loss (entropy loss). In this problem Krishnamoorthy and Gupta [2] proposed an estimator and showed its good performance in a Monte Carlo simulation. They conjecture...

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Bibliographic Details
Published in:Statistics (Berlin, DDR) DDR), 2003-09, Vol.37 (5), p.387-399
Main Author: Sheena†, Yo
Format: Article
Language:English
Subjects:
Minimax
Orthogonally invariant estimator
Precision matrix
Stein's loss
Wishart distribution
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Summary:We consider the orthogonally invariant estimation problem of the inverse of the scale matrix of Wishart distribution using Stein's loss (entropy loss). In this problem Krishnamoorthy and Gupta [2] proposed an estimator and showed its good performance in a Monte Carlo simulation. They conjectured their estimator is minimax. Perron [3] proved its minimaxity for p = 2. In this paper we prove it for p = 3 by using a new method.
ISSN:0233-1888
1029-4910
DOI:10.1080/02331880310001598846