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arXiv · 0704.2500

A universal procedure for aggregating estimators

Alexander Goldenshluger
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Abstract

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. 2009-03-04. A universal procedure for aggregating estimators. https://doi.org/10.1214/00-aos576

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