Estimation of normal covariance matrices parametrized by irreducible symmetric cones under Stein's loss

Authors:
Yoshihiko Konno
Affiliations:
Faculty of Science, Japan Women's University, 2-8-2 Mejirodai Bunkyo-ku, Tokyo 112-8681, Japan
Venue:
Journal of Multivariate Analysis
Year:
2007

Citing 3
Cited 1

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
Inadmissibility of the maximum likelihood estimator of normal covariance matrices with the lattice conditional independence

Journal of Multivariate Analysis

Shrinkage estimators for large covariance matrices in multivariate real and complex normal distributions under an invariant quadratic loss

Journal of Multivariate Analysis

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Abstract

In this paper the problem of estimating a covariance matrix parametrized by an irreducible symmetric cone in a decision-theoretic set-up is considered. By making use of some results developed in a theory of finite-dimensional Euclidean simple Jordan algebras, Bartlett's decomposition and an unbiased risk estimate formula for a general family of Wishart distributions on the irreducible symmetric cone are derived; these results lead to an extension of Stein's general technique for derivation of minimax estimators for a real normal covariance matrix. Specification of the results to the multivariate normal models with covariances which are parametrized by complex, quaternion, and Lorentz types gives minimax estimators for each model.