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

  • Konno, Yoshihiko
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    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.

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    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 98 (2007)
    Issue (Month): 2 (February)
    Pages: 295-316

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    Handle: RePEc:eee:jmvana:v:98:y:2007:i:2:p:295-316
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