PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Statistical estimation via model selection
Lucien Birgé
Indagationes Mathematicae Volume 17, Number 4, pp. 497-537, 2006.

Abstract

The purpose of this paper is to explain the interest and importance of (approximate) models and model selection in Statistics. Starting from the very elementary example of histograms we present a general notion of finite dimensional model for statistical estimation and we explain what type of risk bounds can be expected from the use of one such model. We then give the performance of suitable model selection procedures from a family of such models. We illustrate our point of view by two main examples: the choice of a partition for designing a histogram from an n-sample and the problem of variable selection in the context of Gaussian regression.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
ID Code:4070
Deposited By:Lucien Birgé
Deposited On:25 February 2008