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Density estimation with quadratic loss: a confidence intervals method

Published online by Cambridge University Press:  25 July 2008

Pierre Alquier
Pierre Alquier*
Affiliation:
Laboratoire de Probabilités et Modèles Aléatoires, Université Paris 6, France; alquier@ensae.fr Laboratoire de Statistique, CREST 3, avenue Pierre Larousse, 92240 Malakoff, France.
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Abstract

We propose a feature selection method for density estimation withquadratic loss. This method relies on the study of unidimensionalapproximation models and on the definition of confidence regions forthe density thanks to these models. It is quite general and includescases of interest like detection of relevant wavelets coefficientsor selection of support vectors in SVM. In the general case, weprove that every selected feature actually improves the performanceof the estimator. In the case where features are defined bywavelets, we prove that this method is adaptative near minimax (upto a log term) in some Besov spaces. We end the paper bysimulations indicating that it must be possible to extend theadaptation result to other features.


Keywords

Density estimationsupport vector machineskernel algorithmsthresholding methodswavelets

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Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 12 , 2008 , pp. 438 - 463
Copyright
© EDP Sciences, SMAI, 2008

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