Risk bounds for model selection via penalization
type: Item
instance of: scholarly article
title: Risk bounds for model selection via penalization
zbMATH Open document ID: 0946.62036
author: L. Birgé
author: Pascal Massart
author: Andrew R. Barron
publication date: 1999-06-03T00:00:00Z
review text: The authors develop performance bounds for criteria of model selection, using recent theory for sieves. The model selection criteria are based on an empirical loss or contrast function with an added penalty term roughly proportional to the number of parameters needed to describe the model divided by the number of observations. Most of the presented examples involve density or regression estimation settings, and the authors focus on the problem of estimating the unknown density or regression function. It is shown that the quadratic risk of the minimum penalized empirical contrast estimator is bounded by an index of the accuracy of the sieve. The connection between model selection via penalization and adaptation in the minimax sense is pointed out. Such illustrations of the introduced method as penalized maximum likelihood, projection or least squares estimation are provided. The models involve commonly used finite dimensional expansions such as piecewise polynomials with fixed or variable knots, trigonometric polynomials, wavelets, neural nets, and related nonlinear expansions defined by superposition of ridge functions.
Mathematics Subject Classification ID: 62G05
Mathematics Subject Classification ID: 62G07
Mathematics Subject Classification ID: 41A25
zbMATH DE Number: 1295513
zbMATH Keywords: sieves
zbMATH Keywords: adaptation
zbMATH Keywords: penalized maximum likelihood
zbMATH Keywords: projection
zbMATH Keywords: least squares estimation
reviewed by: Joseph Melamed
MaRDI profile type: Publication
full work available at URL: s004400050210
OpenAlex ID: W1996268356
DOI: 10.1007/S004400050210
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published in: Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete
description: scientific article; zbMATH DE number 1295513