Methods for Improvement in Estimation of a Normal Mean Matrix

Hisayuki Tsukuma and Tatsuya Kubokawa
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Hisayuki Tsukuma: Faculty of Economics, University of Tokyo
Tatsuya Kubokawa: Faculty of Economics, University of Tokyo

No CIRJE-F-378, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: This paper is concerned with the problem of estimating a matrix of means in multivariate normal distributions with an unknown covariance matrix under the quadratic loss function. It is first shown that the modified Efron-Morris estimator is characterized as certain empirical Bayes estimator. This estimator modifies the crude Efron-Morris estimator by adding a scalar shrinkage term. It is next shown that the idea of this modification provides the general method for improvement of estimators, which results in the further improvement of several minimax estimators including the Stein, Dey and Haff estimators. As a new method for improvement, a random combination of the modified Stein and the James-Stein estimators is also proposed and is shown to be minimax. Through Monte Carlo studies for the risk behaviors, it is numerically shown that the proposed, combined estimator inherits the nice risk properties of both individual estimators and thus it has a very favorable risk behavior in a small sample case.

Pages: 27 pages
Date: 2005-09
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:tky:fseres:2005cf378

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