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Large-sample estimation strategies for eigenvalues of a Wishart matrix. (English) Zbl 1093.62543
Summary: The problem of simultaneous asymptotic estimation of eigenvalues of the covariance matrix of a 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.

MSC:
62H12 Estimation in multivariate analysis
62F12 Asymptotic properties of parametric estimators
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