Improved Estimation of Parameter Matrices in a One-Sample and Two-Sample Problems |
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Authors: | Pui Lam Leung Foon Yip Ng |
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Institution: | (1) Department of Statistics, The Chinese University of Hong Kong, Shatin, Hong Kong, China |
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Abstract: | In this paper, the problems of estimating the covariance matrix in a Wishart distribution (refer as one-sample problem) and the scale matrix in a multi-variate F distribution (which arise naturally from a two-sample setting) are considered. A new class of estimators which shrink the eigenvalues towards their harmonic mean is proposed. It is shown that the new estimator dominates the best linear estimator under two scale invariant loss functions. |
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Keywords: | Covariance matrix orthogonally invariant estimator decision-theoretic estimation shrinkage estimator harmonic mean eigenvalues |
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