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

Abstract

Kernel density estimation is a well known method involving a smooth- ing 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 pur- pose of this paper is to study a recently developed bandwidth selection method, called Penalized Comparison to Overfitting (PCO). We first provide new theo- retical 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.