Conditional optimization of the functional computational kernel algorithm for approximating the probability density on the basis of a given sample

The problem of obtaining a numerical functional approximation of probability density on the basis of a given or simulated sample values with a prescribed error level at the minimum cost is considered. A computational algorithm for solving this problem that is a functional version of the kernel estimate of the probability density is proposed. This algorithm is similar to the functional computational kernel statistical algorithm for the approximate solution of the Fredholm integral equation of second kind, for which the theory of conditional optimization was earlier built. In this paper, this theory is built for the constructed functional computational kernel algorithm of approximating the probability density.