Abstract Details
Activity Number:
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361
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Type:
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Contributed
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Date/Time:
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Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
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Sponsor:
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IMS
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Abstract - #309166 |
Title:
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James-Stein Estimation for P Bigger Than N and Unknown Covariance Matrix
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Author(s):
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Didier Chetelat*+ and Martin T Wells
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Companies:
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Cornell University and Cornell University
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Keywords:
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James-Stein ;
large-p-small-n ;
high dimension ;
minimax ;
covariance
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Abstract:
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We consider the problem of estimating the mean vector of a p- variate normal distribution under invariant quadratic loss when the covariance is unknown. In the spirit of the classical James-Stein estimator, we propose a new class of estimators that dominate the trivial estimator X. The proposed estimators depend upon X and an independent Wishart matrix S with n degrees of freedom, even though such a matrix is almost surely singular for p > n. The proof of domination involves the development of some new unbiased estimators of risk for such a setting. In the process, we also exhibit relationships between the amount of domination and the magnitudes of n and p.
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