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Numerical performance of Penalized Comparison to Overfitting for multivariate kernel density estimation

Varet, Suzanne; Lacour, Claire; Massart, Pascal; Rivoirard, Vincent (2019), Numerical performance of Penalized Comparison to Overfitting for multivariate kernel density estimation. https://basepub.dauphine.fr/handle/123456789/18556

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PCO-num.pdf (1.833Mb)
Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-02002275
Date
2019
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Published in
Paris
Pages
50
Metadata
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Author(s)
Varet, Suzanne
Laboratoire de Mathématiques d'Orsay [LM-Orsay]
Lacour, Claire
Laboratoire d'Analyse et de Mathématiques Appliquées [LAMA]
Massart, Pascal
Laboratoire de Mathématiques d'Orsay [LM-Orsay]
Rivoirard, Vincent
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
Kernel density estimation is a well known method involving a smoothing parameter (the bandwidth) that needs to be tuned by the user. Although this method has been widely used the bandwidth selection remains a challenging issue in terms of balancing algorithmic performance and statistical relevance. The purpose of this paper is to compare a recently developped bandwidth selection method for kernel density estimation to those which are commonly used by now (at least those which are implemented in the R-package). This new method is called Penalized Comparison to Overfitting (PCO). It has been proposed by some of the authors of this paper in a previous work devoted to its statistical relevance from a purely theoretical perspective. It is compared here to other usual bandwidth selection methods for univariate and also multivariate kernel density estimation on the basis of intensive simulation studies. In particular, cross-validation and plug-in criteria are numerically investigated and compared to PCO. The take home message is that PCO can outperform the classical methods without algorithmic additionnal cost.
Subjects / Keywords
Multivariate density estimation; Bandwidth selection; Kernel-based density estimation

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