  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.
