Choice of approximation bases used in computational functional algorithms for approximating probability densities for a given sample
A.V. Voytishek1, N.K. Shlimbetov2
1Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia
2Novosibirsk State University, Novosibirsk, Russia
Keywords: computational nonparametric estimation of probability density for a given sample, computational functional kernel algorithm, computational functional projection algorithm, multi-dimensional analogue of frequency polygon, Strang-Fix approximation, multi-linear approximation, conditional optimization of computational functional algorithms
Abstract
In this paper we formulate the requirements for choosing approximation bases in constructing cost-effective optimized computational (numerical) functional algorithms for approximating probability densities for a given sample, with special attention to stability and approximation of the bases. It is shown that to meet the requirements and construct efficient approaches to conditional optimization of the numerical schemes, the best choice is a multi-linear approximation and a corresponding special case for both kernel and projection computational algorithms for nonparametric density estimation, which is a multidimensional analogue of the frequency polygon.
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