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Sharp Oracle Inequalities for Aggregation of Affine Estimators

Abstract : We consider the problem of combining a (possibly uncountably infinite) set of affine estimators in non-parametric regression model with heteroscedastic Gaussian noise. Focusing on the exponentially weighted aggregate, we prove a PAC-Bayesian type inequality that leads to sharp oracle inequalities in discrete but also in continuous settings. The framework is general enough to cover the combinations of various procedures such as least square regression, kernel ridge regression, shrinking estimators and many other estimators used in the literature on statistical inverse problems. As a consequence, we show that the proposed aggregate provides an adaptive estimator in the exact minimax sense without neither discretizing the range of tuning parameters nor splitting the set of observations. We also illustrate numerically the good performance achieved by the exponentially weighted aggregate.
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Contributeur : Arnak Dalalyan Connectez-vous pour contacter le contributeur
Soumis le : lundi 27 février 2012 - 22:47:14
Dernière modification le : samedi 19 juin 2021 - 03:33:31
Archivage à long terme le : : lundi 28 mai 2012 - 03:05:36


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Arnak S. Dalalyan, Joseph Salmon. Sharp Oracle Inequalities for Aggregation of Affine Estimators. Annals of Statistics, Institute of Mathematical Statistics, 2012, 40 (4), pp.2327-2355. ⟨10.1214/12-AOS1038⟩. ⟨hal-00587225v3⟩



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