Mathematics – Statistics Theory
Scientific paper
2005-11-18
Annals of Statistics 2008, Vol. 36, No. 5, 2183-2206
Mathematics
Statistics Theory
Published in at http://dx.doi.org/10.1214/07-AOS546 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Scientific paper
10.1214/07-AOS546
Given a finite collection of estimators or classifiers, we study the problem of model selection type aggregation, that is, we construct a new estimator or classifier, called aggregate, which is nearly as good as the best among them with respect to a given risk criterion. We define our aggregate by a simple recursive procedure which solves an auxiliary stochastic linear programming problem related to the original nonlinear one and constitutes a special case of the mirror averaging algorithm. We show that the aggregate satisfies sharp oracle inequalities under some general assumptions. The results are applied to several problems including regression, classification and density estimation.
Juditsky Anatoli
Rigollet Philippe
Tsybakov Alexandre B.
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