Estimation of Root-Mean-Square Errors of Computer Functional Kernel and Projection Algorithms for the Approximation of Probability Densities for a Given Sample

In this paper, we consider problems of obtaining upper bounds for components of root-mean-square errors for computational constructions of approximation of an unknown probability density for a given sample. Examples are the computational functional kernel and projection algorithms as well as their important special case—the multidimensional analog of the frequency polygon. These bounds are then used in choosing those versions of the kernel and projection algorithms that provide a given level of error in a density approximation.