Methods for Improvement in Estimation of a Normal Mean Matrix
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.
|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
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Dey, Dipak K., 1987. "Improved estimation of a multinormal precision matrix," Statistics & Probability Letters, Elsevier, vol. 6(2), pages 125-128, November.
- Ghosh, Malay & Shieh, Gwowen, 1991. "Empirical Bayes minimax estimators of matrix normal means," Journal of Multivariate Analysis, Elsevier, vol. 38(2), pages 306-318, August.
- Loh, Wei-Liem, 1991. "Estimating covariance matrices II," Journal of Multivariate Analysis, Elsevier, vol. 36(2), pages 163-174, February.
- Konno, Yoshihiko, 1991. "On estimation of a matrix of normal means with unknown covariance matrix," Journal of Multivariate Analysis, Elsevier, vol. 36(1), pages 44-55, January.
- Bilodeau, Martin & Kariya, Takeaki, 1989. "Minimax estimators in the normal MANOVA model," Journal of Multivariate Analysis, Elsevier, vol. 28(2), pages 260-270, February.
When requesting a correction, please mention this item's handle: RePEc:tky:fseres:2005cf378. See general 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.