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Histogram selection in non gaussian regression

Marie Sauvé 1
1 SELECT - Model selection in statistical learning
LMO - Laboratoire de Mathématiques d'Orsay, Inria Saclay - Ile de France
Abstract : We deal with the problem of choosing an histogram estimator of a regression function $s$ mapping $\mathcalX$ into $\mathbbR$. We adopt the non asymptotic approach of model selection via penalization developped by Birgé and Massart, but we do not assume that the observations are gaussian variables. We consider a collection of partitions of $\mathcalX$, with possibly exponential complexity, and the corresponding collection of histogram estimators. We propose a penalized least squares criterion which selects a partition whose associated estimator performs approximately as well as the best one, in the sense that its quadratic risk is close to the infimum of the risks. The risk bound we provide is non asymptotic.
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Submitted on : Tuesday, May 23, 2006 - 4:48:34 PM
Last modification on : Wednesday, September 16, 2020 - 5:07:09 PM
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Marie Sauvé. Histogram selection in non gaussian regression. [Research Report] RR-5911, INRIA. 2006. ⟨inria-00071351⟩

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