Mathematics – Statistics Theory
Scientific paper
2007-04-19
Annals of Statistics 2009, Vol. 37, No. 1, 542-568
Mathematics
Statistics Theory
Published in at http://dx.doi.org/10.1214/00-AOS576 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Scientific paper
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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