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Sibirskii Zhurnal Vychislitel'noi Matematiki, 2024, Volume 27, Number 2, Pages 147–164
DOI: https://doi.org/10.15372/SJNM20240202
(Mi sjvm867)
 

Choice of approximation bases used in computational functional algorithms for approximating probability densities for a given sample

A. V. Voitisheka, N. K. Shlimbetovb

a Institute of Computational Mathematics and Mathematical Geophysics of Siberian Branch of Russian Academy of Sciences, Novosibirsk, Russia
b Novosibirsk State University, Russia
References:
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.
Key words: 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.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 0251-2021-0002
Received: 02.01.2024
Revised: 10.01.2024
Accepted: 04.03.2024
Bibliographic databases:
Document Type: Article
UDC: 519.245
Language: Russian
Citation: A. V. Voitishek, N. K. Shlimbetov, “Choice of approximation bases used in computational functional algorithms for approximating probability densities for a given sample”, Sib. Zh. Vychisl. Mat., 27:2 (2024), 147–164
Citation in format AMSBIB
\Bibitem{VoiShl24}
\by A.~V.~Voitishek, N.~K.~Shlimbetov
\paper Choice of approximation bases used in computational functional algorithms for approximating probability densities for a given sample
\jour Sib. Zh. Vychisl. Mat.
\yr 2024
\vol 27
\issue 2
\pages 147--164
\mathnet{http://mi.mathnet.ru/sjvm867}
\crossref{https://doi.org/10.15372/SJNM20240202}
\edn{https://elibrary.ru/UPAPTG}
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