Unified Improvements in Estimation of a Normal Covariance Matrix in High and Low Dimesions

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

No CIRJE-F-937, CIRJE F-Series from CIRJE, Faculty of Economics, University of Tokyo

Abstract: The problem of estimating a covariance matrix in multivariate linear regression models is addressed in a decision-theoretic framework. Although a standard loss function is the Stein loss, it is not available in the case of a high dimension. In this paper, a new type of a quadratic loss function, called the intrinsic loss, is suggested, and unified dominance results are derived under the loss, irrespective of order of the dimension, the sample size and the rank of the regression coefficients matrix. Especially, using the Stein-Haff identity, we develop a key inequality which is useful for constructing a truncated and improved estimator based on the information contained in the sample means or the ordinary least squares estimator of the regression coefficients.

Pages: 27 pages
Date: 2014-08
New Economics Papers: this item is included in nep-ecm
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