Estimation of root-mean-square errors of computer functional kernel and projection algorithms for approximation of probability densities for a given sample
N.Kh. Shlimbetov1, A.V. Voytishek2
1Novosibirsk State University, Novosibirsk, Russia
2Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia
Keywords: computational functional kernel algorithm, computational functional projection algorithm, multi-dimensional analog of frequency polygon, root-mean-square error, approximation component, bias component, stochastic component, conditional optimization problem
Abstract
In this paper, we consider problems of obtaining upper bounds for the components of root-mean-square errors for computational constructions of approximation of an unknown probability density for a given sample. Examples are the computer 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 such versions of kernel and projection algorithms that provide a given level of error in a density approximation.
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