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.