Estimating the probability density by the stochastic regularization method

The stochastic regularization method leads to nonparametric estimates of probability densities of the projection, Rosenblatt — Parsen, splyne, and histogram types. Methods are considered of choosing the smoothing parameter; the smoothing method is shown to be optimal for the Rosenblatt — Parsen estimate. In estimating the multidimensional density by the latter method a technique is proposed of choosing the kernel function of a certain type.