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Activity Number:
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558
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Type:
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Contributed
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Date/Time:
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Thursday, August 6, 2009 : 8:30 AM to 10:20 AM
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Sponsor:
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IMS
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| Abstract - #304027 |
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Title:
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General Maximum Likelihood Empirical Bayes Estimation of Normal Means
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Author(s):
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Wenhua Jiang*+ and Cun-Hui Zhang
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Companies:
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Rutgers University and Rutgers University
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Address:
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110 Frelinghuysen Road, Piscataway, NJ, 08854,
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Keywords:
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compound estimation ; empirical Bayes ; adaptive estimation ; white noise ; shrinkage estimator ; threshold estimator
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Abstract:
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We propose a general maximum likelihood empirical Bayes (GMLEB) method for the estimation of a mean vector based on observations with iid normal errors. We prove that the risk of the GMLEB estimator is within an infinitesimal fraction of the ideal Bayes risk when this risk of greater order than $(\log n)^5/n$ depending on the magnitude of the weak $\ell_p$ norm of the unknown means. We also prove the adaptive minimaxity of the GMLEB estimator over a broad collection of $\ell_p$ balls. We provide an EM algorithm for the computation of the GMLEB. Our simulation results affirm that by aiming at the minimum risk of all separable estimators, the greedier general EB approach realizes significant risk reduction over state-of-the-art threshold methods for the unknown signal vectors of different degrees of sparsity.
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