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

¹ Université Paris-Saclay, CNRS, Laboratoire de mathématiques d’Orsay, 91405 Orsay, France
² LAMA, Univ Gustave Eiffel, Univ Paris Est Creteil, CNRS, 77447 Marne-la-Vallée, France
³ CEREMADE, CNRS, UMR 7534, Université Paris-Dauphine, PSL University, 75016 Paris, France

^* Corresponding author: claire.lacour@u-pem.fr

Received: 17 September 2021
Accepted: 18 November 2022

Abstract

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.