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

TL;DR

This paper evaluates the performance of the Penalized Comparison to Overfitting (PCO) method for bandwidth selection in multivariate kernel density estimation, showing it can outperform traditional methods without extra computational cost.

Contribution

It provides an empirical comparison of PCO against standard bandwidth selection methods in multivariate kernel density estimation, demonstrating its effectiveness.

Findings

PCO often outperforms classical methods in simulations

PCO achieves better balance between accuracy and computational efficiency

Traditional methods are sometimes less effective in multivariate settings

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 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.