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Article Dans Une Revue ESAIM: Probability and Statistics Année : 2023

Numerical performance of penalized comparison to overfitting for multivariate kernel density estimation

Résumé

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 study a recently developed bandwidth selection method, called Penalized Comparison to Overfitting (PCO). We first provide new theoretical guarantees by proving that PCO performed with non-diagonal bandwidth matrices is optimal in the oracle and minimax approaches. PCO is then compared to other usual bandwidth selection methods (at least those which are implemented in the R-package) 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 additional cost.
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Origine : Publication financée par une institution

Dates et versions

hal-04131767 , version 1 (02-02-2019)
hal-04131767 , version 2 (17-06-2023)

Identifiants

Citer

Suzanne Varet, Claire Lacour, Pascal Massart, Vincent Rivoirard. Numerical performance of penalized comparison to overfitting for multivariate kernel density estimation. ESAIM: Probability and Statistics, 2023, 27, pp.621-667. ⟨10.1051/ps/2022018⟩. ⟨hal-04131767v2⟩
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