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August 2009 Nonparametric empirical Bayes and compound decision approaches to estimation of a high-dimensional vector of normal means
Lawrence D. Brown, Eitan Greenshtein
Ann. Statist. 37(4): 1685-1704 (August 2009). DOI: 10.1214/08-AOS630

Abstract

We consider the classical problem of estimating a vector μ=(μ1, …, μn) based on independent observations YiN(μi, 1), i=1, …, n.

Suppose μi, i=1, …, n are independent realizations from a completely unknown G. We suggest an easily computed estimator μ̂, such that the ratio of its risk E(μ̂μ)2 with that of the Bayes procedure approaches 1. A related compound decision result is also obtained.

Our asymptotics is of a triangular array; that is, we allow the distribution G to depend on n. Thus, our theoretical asymptotic results are also meaningful in situations where the vector μ is sparse and the proportion of zero coordinates approaches 1.

We demonstrate the performance of our estimator in simulations, emphasizing sparse setups. In “moderately-sparse” situations, our procedure performs very well compared to known procedures tailored for sparse setups. It also adapts well to nonsparse situations.

Citation

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Lawrence D. Brown. Eitan Greenshtein. "Nonparametric empirical Bayes and compound decision approaches to estimation of a high-dimensional vector of normal means." Ann. Statist. 37 (4) 1685 - 1704, August 2009. https://doi.org/10.1214/08-AOS630

Information

Published: August 2009
First available in Project Euclid: 18 June 2009

zbMATH: 1166.62005
MathSciNet: MR2533468
Digital Object Identifier: 10.1214/08-AOS630

Subjects:
Primary: 62C12, 62C25

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 4 • August 2009
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