Methods for Improvement in Estimation of a Normal Mean Matrix
AbstractThis 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-378.
Length: 27 pages
Date of creation: Sep 2005
Date of revision:
Contact details of provider:
Postal: Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033
Web page: http://www.cirje.e.u-tokyo.ac.jp/index.html
More information through EDIRC
This paper has been announced in the following NEP Reports:
You can help add them by filling out this form.
reading list or among the top items on IDEAS.Access and download statisticsgeneral information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CIRJE administrative office).
If references are entirely missing, you can add them using this form.