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

Multivariate Universal Local Linear Kernel Estimators in Nonparametric Regression: Uniform Consistency Full article

Journal

Mathematics
, E-ISSN: 2227-7390

Output data

Year: 2024, Volume: 12, Number: 12, Article number : 1890, Pages count : DOI: 10.3390/math12121890

Tags

nonparametric regression; local linear estimator; uniform consistency; fixed design; random design; strongly dependent design elements

Authors

Linke Yuliana ^1,2 , Borisov Igor ^1,2 , Ruzankin Pavel ^1,2 , Kutsenko Vladimir ^3,4 , Yarovaya Elena ^3,4 , Shalnova Svetlana ³

Affiliations

1	Department of Probability and Mathematical Statistics, Novosibirsk State University, 630090 Novosibirsk, Russia
2	Sobolev Institute of Mathematics, 630090 Novosibirsk, Russia
3	Department of Epidemiology of Noncommunicable Diseases, National Medical Research Center for Therapy and Preventive Medicine, 101990 Moscow, Russia
4	Department of Probability Theory, Lomonosov Moscow State University, 119234 Moscow, Russia

Funding (1)

Министерство науки и высшего образования РФ
Mathematical Center in Akademgorodok

075-15-2019-1613, 075-15-2022-281

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.

Linke Y. , Borisov I. , Ruzankin P. , Kutsenko V. , Yarovaya E. , Shalnova S.
Multivariate Universal Local Linear Kernel Estimators in Nonparametric Regression: Uniform Consistency
Mathematics. 2024. V.12. N12. 1890 . DOI: 10.3390/math12121890 WOS Scopus РИНЦ OpenAlex

Submitted:	May 15, 2024
Accepted:	Jun 13, 2024
Published print:	Jun 18, 2024
Published online:	Jun 18, 2024

Web of science:	WOS:001256737200001
Scopus:	2-s2.0-85197850857
Elibrary:	68408843
OpenAlex:	W4399809942

DB	Citing
Web of science	1
Scopus	2