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.
In: Numerical Analysis and Applications, Vol. 19, No. 2, 26.07.2026, p. 90-101.Research output: Contribution to journal › Article › peer-review
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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