Nonparametric methods for restoring the probability densities

The paper is cencerned with restoration of a continuous probability density as an ill-posed (according to Hadamar) problem of numerical differentiation for an emprirical distribution function. The solution conditions and conditions for convergence of Paezen estimates are the same. An algorithm is proposed whereby the probability density is restored from a sample of limited size. The method of ordered risk minimization is used in the algorithm.