Bandwidth selection in nonparametric estimator of density derivative by smoothed cross-validation method

In the nonparametric kernel estimation of the unknown probability densities and their derivatives there exist several methods for estimation of the kernel function bandwidth of which the $CV$ and $SCV$ methods of cross-validation are most simple and suitable. The former method was developed both for the density itself and its derivatives; the latter one, for density only. Yet it generates estimates with a higher rate of convergence and substantially smaller scatter. For the problem of nonparametric restoration of the density derivative from an independent sample, a data-based estimate of the kernel function bandwidth was constructed.