TY - JOUR

T1 - Multivariate Universal Local Linear Kernel Estimators in Nonparametric Regression: Uniform Consistency

AU - Linke, Yuliana

AU - Borisov, Igor

AU - Ruzankin, Pavel

AU - Kutsenko, Vladimir

AU - Yarovaya, Elena

AU - Shalnova, Svetlana

N1 - The study of Y. Linke and I. Borisov is supported by the Mathematical Center in Akademgorodok under agreement no. 075-15-2022-281 with the Ministry of Science and Higher Education of the Russian Federation.

PY - 2024/6

Y1 - 2024/6

N2 - In this paper, for a wide class of nonparametric regression models, new local linear kernel estimators are proposed that are uniformly consistent under close-to-minimal and visual conditions on design points. These estimators are universal in the sense that their designs can be either fixed and not necessarily satisfying the traditional regularity conditions, or random, while not necessarily consisting of independent or weakly dependent random variables. With regard to the design elements, only dense filling of the regression function domain with the design points without any specification of their correlation is assumed. This study extends the dense data methodology and main results of the authors’ previous work for the case of regression functions of several variables.

AB - In this paper, for a wide class of nonparametric regression models, new local linear kernel estimators are proposed that are uniformly consistent under close-to-minimal and visual conditions on design points. These estimators are universal in the sense that their designs can be either fixed and not necessarily satisfying the traditional regularity conditions, or random, while not necessarily consisting of independent or weakly dependent random variables. With regard to the design elements, only dense filling of the regression function domain with the design points without any specification of their correlation is assumed. This study extends the dense data methodology and main results of the authors’ previous work for the case of regression functions of several variables.

KW - fixed design

KW - local linear estimator

KW - nonparametric regression

KW - random design

KW - strongly dependent design elements

KW - uniform consistency

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85197850857&origin=inward&txGid=0c6179e429a4a7f270fdf2d073c3b119

UR - https://www.mendeley.com/catalogue/c24d5e11-e462-394c-a4e6-18599116b570/

U2 - 10.3390/math12121890

DO - 10.3390/math12121890

M3 - Article

VL - 12

JO - Mathematics

JF - Mathematics

SN - 2227-7390

IS - 12

M1 - 1890

ER -