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Metrika

, Volume 47, Issue 1, pp 35–45 | Cite as

Large-sample estimation strategies for eigenvalues of a Wishart matrix

  • S. E. Ahmed
Article

Abstract

The problem of simultaneous asymptotic estimation of eigenvalues of covariance matrix of Wishart matrix is considered under a weighted quadratic loss function. James-Stein type of estimators are obtained which dominate the sample eigenvalues. The relative merits of the proposed estimators are compared to the sample eigenvalues using asymptotic quadratic distributional risk under loal alternatives. It is shown that the proposed estimators are asymptotically superior to the sample eigenvalues. Further, it is demonstrated that the James-Stein type estimator is dominated by its truncated part.

Key Words and Phrases

Wishart distribution eigenvalues covariance matrix James-Stein type estimators positive-part estimators asymptotic quadratic bias and risk 

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Copyright information

© Physica-Verlag 1998

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of Regina, ReginaSaskatchewanCanada

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