A Unified Approach to Estimating a Normal Mean Matrix in High and Low Dimensions
Abstractã€€ã€€ This paper addresses the problem of estimating the normal mean matrix with an unknown covariance matrix. Motivated by an empirical Bayes method, we suggest a uni ed form of the Efron-Morris type estimators based on the Moore-Penrose inverse. This form not only can be de ned for any dimension and any sample size, but also can contain the Efron-Morris type or Baranchik type estimators suggested so far in the literature. Also, the uni ed form suggests a general class of shrinkage estimators. For shrinkage estimators within the general class, a uni ed expression of unbiased estimators of the risk functions is derived regardless of the dimension of covariance matrix and the size of the mean matrix. An analytical dominance result is provided for a positive-part rule of the shrinkage estimators.
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Bibliographic InfoPaper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-926.
Length: 23 pages
Date of creation: Mar 2014
Date of revision:
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This paper has been announced in the following NEP Reports:
- NEP-ALL-2014-04-11 (All new papers)
- NEP-ECM-2014-04-11 (Econometrics)
- NEP-GER-2014-04-11 (German Papers)
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