Estimating the covariance matrix: a new approach

Authors:
T. Kubokawa;M. S. Srivastava
Affiliations:
Faculty of Economics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan;Department of Statistics, University of Toronto, 100 St. George Street, Toronto, Ont., Canada M5S 3G3
Venue:
Journal of Multivariate Analysis
Year:
2003

Citing 2
Cited 3

Inadmissability of non-order-preserving orthogonally invariant estimators of the covariance matrix in the case of Stein's loss

Journal of Multivariate Analysis
Minimax estimators of a covariance matrix

Journal of Multivariate Analysis

Best approximation of the identity mapping: The case of variable finite memory

Journal of Approximation Theory
Estimation of covariance matrices in fixed and mixed effects linear models

Journal of Multivariate Analysis
Optimal multilinear estimation of a random vector under constraints of causality and limited memory

Computational Statistics & Data Analysis

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Abstract

In this paper, we consider the problem of estimating the covariance matrix and the generalized variance when the observations follow a nonsingular multivariate normal distribution with unknown mean. A new method is presented to obtain a truncated estimator that utilizes the information available in the sample mean matrix and dominates the James-Stein minimax estimator. Several scale equivariant minimax estimators are also given. This method is then applied to obtain new truncated and improved estimators of the generalized variance; it also provides a new proof to the results of Shorrock and Zidek (Ann. Statist. 4 (1976) 629) and Sinha (J. Multivariate Anal. 6 (1976) 617).