Numerical performance of Penalized Comparison to Overfitting for multivariate kernel density estimation
Varet, Suzanne; Lacour, Claire; Massart, Pascal; Rivoirard, Vincent (2023), Numerical performance of Penalized Comparison to Overfitting for multivariate kernel density estimation, ESAIM. Probability and Statistics, 27, p. 621 - 667. 10.1051/ps/2022018
TypeArticle accepté pour publication ou publié
Journal nameESAIM. Probability and Statistics
MetadataShow full item record
Laboratoire de Mathématiques d'Orsay [LMO]
Laboratoire Analyse et Mathématiques Appliquées [LAMA]
Statistique mathématique et apprentissage [CELESTE]
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 / KeywordsMultivariate density estimation; Bandwidth selection; Kernel-based density estimation
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