English

A universal procedure for aggregating estimators

Statistics Theory 2009-03-04 v3 Statistics Theory

Abstract

In this paper we study the aggregation problem that can be formulated as follows. Assume that we have a family of estimators F\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 F\mathcal{F}. We derive oracle inequalities and show that they are unimprovable in some sense. Numerical results demonstrate good practical behavior of the procedure.

Keywords

Cite

@article{arxiv.0704.2500,
  title  = {A universal procedure for aggregating estimators},
  author = {Alexander Goldenshluger},
  journal= {arXiv preprint arXiv:0704.2500},
  year   = {2009}
}
R2 v1 2026-06-21T08:20:07.727Z