Year: 2008
Type: article
Abstract: We deal with the problem of choosing a piecewise constant estimator of a regression function s mapping into . We consider a non Gaussian regression framework with deterministic design points, and we adopt the non asymptotic approach of model selection via penalization developed by Birgé and Massart. Given a collection of partitions of , with possibly exponential complexity, and the corresponding collection of piecewise constant 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.
Source: ESAIM Probability and Statistics
DOI: 10.1051/ps:2008002
Author: Marie Sauvé
Institutions: Université Paris-Sud, Laboratoire de Mathématiques d'Orsay
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: bronze
OpenAlex ID: W2171656668