Density estimation with quadratic loss: a confidence intervals method

Pierre Alquier (1, 2)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 CREST - Centre de Recherche en Économie et Statistique

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.

Mots clés: Density estimation; statistical learning; confidence regions; thresholding methods; support vector machines

Domaines: Statistiques [math.ST]

Pierre Alquier. Density estimation with quadratic loss: a confidence intervals method. 2006. ⟨hal-00020740⟩