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February 2009 A universal procedure for aggregating estimators
Alexander Goldenshluger
Ann. Statist. 37(1): 542-568 (February 2009). DOI: 10.1214/00-AOS576


In this paper we study the aggregation problem that can be formulated as follows. Assume that we have a family of estimators $\mathcal{F}$ built on the basis of available observations. The goal is to construct a new estimator whose risk is as close as possible to that of the best estimator in the family. We propose a general aggregation scheme that is universal in the following sense: it applies for families of arbitrary estimators and a wide variety of models and global risk measures. The procedure is based on comparison of empirical estimates of certain linear functionals with estimates induced by the family $\mathcal{F}$. We derive oracle inequalities and show that they are unimprovable in some sense. Numerical results demonstrate good practical behavior of the procedure.


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Alexander Goldenshluger. "A universal procedure for aggregating estimators." Ann. Statist. 37 (1) 542 - 568, February 2009.


Published: February 2009
First available in Project Euclid: 16 January 2009

zbMATH: 1155.62018
MathSciNet: MR2488362
Digital Object Identifier: 10.1214/00-AOS576

Primary: 62G08
Secondary: 62G05 , 62G20

Keywords: Aggregation , lower bound , normal means model , Oracle inequalities , sparse vectors , White noise model

Rights: Copyright © 2009 Institute of Mathematical Statistics

Vol.37 • No. 1 • February 2009
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