Volume 27, 2023
|Page(s)||621 - 667|
|Published online||16 June 2023|
Numerical performance of penalized comparison to overfitting for multivariate kernel density estimation
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: firstname.lastname@example.org
Accepted: 18 November 2022
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.
Mathematics Subject Classification: 62G07 / 62-08 / 62H12
Key words: Multivariate density estimation / Kernel-based density estimation / Bandwidth selection
© The authors. Published by EDP Sciences, SMAI 2023
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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