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2013 Optimal model selection in heteroscedastic regression using piecewise polynomial functions
Adrien Saumard
Electron. J. Statist. 7: 1184-1223 (2013). DOI: 10.1214/13-EJS803

Abstract

We consider the estimation of a regression function with random design and heteroscedastic noise in a nonparametric setting. More precisely, we address the problem of characterizing the optimal penalty when the regression function is estimated by using a penalized least-squares model selection method. In this context, we show the existence of a minimal penalty, defined to be the maximum level of penalization under which the model selection procedure totally misbehaves. The optimal penalty is shown to be twice the minimal one and to satisfy a non-asymptotic pathwise oracle inequality with leading constant almost one. Finally, the ideal penalty being unknown in general, we propose a hold-out penalization procedure and show that the latter is asymptotically optimal.

Citation

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Adrien Saumard. "Optimal model selection in heteroscedastic regression using piecewise polynomial functions." Electron. J. Statist. 7 1184 - 1223, 2013. https://doi.org/10.1214/13-EJS803

Information

Published: 2013
First available in Project Euclid: 25 April 2013

zbMATH: 1337.62083
MathSciNet: MR3056072
Digital Object Identifier: 10.1214/13-EJS803

Subjects:
Primary: 62G08, 62G09, 62J02

Rights: Copyright © 2013 The Institute of Mathematical Statistics and the Bernoulli Society

JOURNAL ARTICLE
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