2006/03/14 by Pierre Alquier, Alquier, Pierre
Computer Science · Mathematics · #62G07 #62G15 #68T05 #Bayesian Methods and Mixture Models #FOS: Mathematics #Machine Learning and Algorithms #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #msc:62G07 #msc:62G15 #msc:68T05 #stat.TH
paper · pdf · doi:10.48550/arxiv.math/0603349
arxiv created 2006/03/14 · openalex publication_date 2006/03/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In a previous article, a least square regression estimation procedure was proposed: first, we condiser a family of functions and study the properties of an estimator in every unidimensionnal model defined by one of these functions; we then show how to aggregate these estimators. The purpose of this paper is to extend this method to the case of density estimation. We first give a general overview of the method, adapted to the density estimation problem. We then show that this leads to adaptative estimators, that means that the estimator reaches the best possible rate of convergence (up to a log factor). Finally we show some ways to improve and generalize the method.