Slope heuristics and V-Fold model selection in heteroscedastic regression using strongly localized bases

Fabien Navarro () and Adrien Saumard ()
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Fabien Navarro: CREST;ENSAI
Adrien Saumard: CREST;ENSAI

No 2017-67, Working Papers from Center for Research in Economics and Statistics

Abstract: We investigate the optimality for model selection of the so-called slope heuristics, V -fold cross-validation and V -fold penalization in a heteroscedatic with random design regression context. We consider a new class of linear models that we call strongly localized bases and that generalize histograms, piecewise polynomials and compactly supported wavelets. We derive sharp oracle inequalities that prove the asymptotic optimality of the slope heuristics—when the optimal penalty shape is known—and V -fold penalization. Furthermore, V -fold cross-validation seems to be suboptimal for a ?xed value of V since it recovers asymptotically the oracle learned from a sample size equal to 1-V -1 of the original amount of data. Our results are based on genuine concentration inequalities for the true and empirical excess risks that are of independent interest. We show in our experiments the good behavior of the slope heuristics for the selection of linear wavelet models. Furthermore, V -fold cross-validation and V -fold penalization have comparable e?ciency.

Keywords: Nonparametric regression; heteroscedastic noise; random design; model selection; cross-validation; wavelets (search for similar items in EconPapers)
Pages: 36 pages
Date: 2017
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Citations: View citations in EconPapers (2)

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