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 invariant quadratic loss. It is first shown that the modified Efron-Morris estimator is characterized as a 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 a general method for improvement of estimators, which results in the further improvement on several minimax estimators. As a new method for improvement, an adaptive combination of the modified Stein and the James-Stein estimators is also proposed and is shown to be minimax. Through Monte Carlo studies of 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. Finally, the application to a two-way layout MANOVA model with interactions is discussed.
If 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.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 98 (2007)
Issue (Month): 8 (September)
|Contact details of provider:|| Web page: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description|
|Order Information:|| Postal: http://www.elsevier.com/wps/find/supportfaq.cws_home/regional|
References listed on IDEAS
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.
- Hisayuki Tsukuma & Tatsuya Kubokawa, 2005. "Methods for Improvement in Estimation of a Normal Mean Matrix," CIRJE F-Series CIRJE-F-378, CIRJE, Faculty of Economics, University of Tokyo.
- Bilodeau, Martin & Kariya, Takeaki, 1989. "Minimax estimators in the normal MANOVA model," Journal of Multivariate Analysis, Elsevier, vol. 28(2), pages 260-270, 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.
When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:98:y:2007:i:8:p:1592-1610. 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: (Shamier, Wendy)
If references are entirely missing, you can add them using this form.