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

Standard

Estimation of Root-Mean-Square Errors of Computer Functional Kernel and Projection Algorithms for the Approximation of Probability Densities for a Given Sample. / Shlimbetov, N. Kh.; Voytishek, A. V.

в: Numerical Analysis and Applications, Том 19, № 2, 26.07.2026, стр. 90-101.

Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование

BibTeX

@article{25fdddd3823345e3a4f04ee731bf32fa,

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

abstract = "ABSTRACT: 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.",

keywords = "approximation component, bias component, computational functional kernel algorithm, computational functional projection algorithm, conditional optimization problem, multidimensional analog of frequency polygon, root-mean-square error, stochastic component, вычислительный функциональный ядерный алгоритм, вычислительный функциональный проекционный алгоритм, многомерный аналог частотного многоугольника, среднеквадратичная ошибка, аппроксимация компонента, компонента смещения, стохастическая компонента, задача условной оптимизации",

author = "Shlimbetov, {N. Kh.} and Voytishek, {A. V.}",

note = "Shlimbetov, N., Voytishek, A. Estimation of Root-Mean-Square Errors of Computer Functional Kernel and Projection Algorithms for the Approximation of Probability Densities for a Given Sample. Numer. Analys. Appl. 19, 90–101 (2026). https://doi.org/10.1134/S1995423926020023 The investigations were carried out within the framework of a state assignment of ICM & MG SB RAS (project no. FWNM-2025-0002).",

year = "2026",

month = jul,

day = "26",

doi = "10.1134/S1995423926020023",

language = "English",

volume = "19",

pages = "90--101",

journal = "Numerical Analysis and Applications",

issn = "1995-4239",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "2",

}

RIS

TY - JOUR

T1 - Estimation of Root-Mean-Square Errors of Computer Functional Kernel and Projection Algorithms for the Approximation of Probability Densities for a Given Sample

AU - Shlimbetov, N. Kh.

AU - Voytishek, A. V.

N1 - Shlimbetov, N., Voytishek, A. Estimation of Root-Mean-Square Errors of Computer Functional Kernel and Projection Algorithms for the Approximation of Probability Densities for a Given Sample. Numer. Analys. Appl. 19, 90–101 (2026). https://doi.org/10.1134/S1995423926020023 The investigations were carried out within the framework of a state assignment of ICM & MG SB RAS (project no. FWNM-2025-0002).

PY - 2026/7/26

Y1 - 2026/7/26

N2 - ABSTRACT: 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.

AB - ABSTRACT: 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.

KW - approximation component

KW - bias component

KW - computational functional kernel algorithm

KW - computational functional projection algorithm

KW - conditional optimization problem

KW - multidimensional analog of frequency polygon

KW - root-mean-square error

KW - stochastic component

KW - вычислительный функциональный ядерный алгоритм

KW - вычислительный функциональный проекционный алгоритм

KW - многомерный аналог частотного многоугольника

KW - среднеквадратичная ошибка

KW - аппроксимация компонента

KW - компонента смещения

KW - стохастическая компонента

KW - задача условной оптимизации

UR - https://www.mendeley.com/catalogue/744821cf-d84b-30c0-bffa-046f83a705a4/

UR - https://www.scopus.com/pages/publications/105046197224

U2 - 10.1134/S1995423926020023

DO - 10.1134/S1995423926020023

M3 - Article

VL - 19

SP - 90

EP - 101

JO - Numerical Analysis and Applications

JF - Numerical Analysis and Applications

SN - 1995-4239

IS - 2

ER -

ID: 85023262