Multivariate Universal Local Linear Kernel Estimators in Nonparametric Regression: Simulations and Real Data Processing | Sciact - Система учета научной деятельности ИМ СО РАН

Multivariate Universal Local Linear Kernel Estimators in Nonparametric Regression: Simulations and Real Data Processing Научная публикация

Журнал

Sankhya A
ISSN: 0976-836X , E-ISSN: 0976-8378

Вых. Данные

Год: 2025, Страницы: 1-28 Страниц : 28 DOI: 10.1007/s13171-025-00391-z

Ключевые слова

Universal local linear model, Universal local constant model, Local linear model, Local constant model, Generalized additive models (GAM), Multivariate adaptive regression splines (MARS), LOESS, Nonparametric regression, Kernel-type estimator, Uniform consistency, Fixed design, Random design, Strongly dependent design elements.

Авторы

Linke Y.Y. ¹ , Borisov I.S. ¹ , Ruzankin P.S. ¹ , Kutsenko V.A. ³ , Yarovaya E.B. ^2,3 , Shalnova S.A. ³

Организации

1	Sobolev Institute of Mathematics, Novosibirsk, Russia
2	Lomonosov Moscow State University, Moscow
3	Russia National Medical Research Center for Therapy and Preventive Medicine of the Ministry of Healthcare of the Russian Federation, Moscow, Russia

Информация о финансировании (1)

Институт математики им. С.Л. Соболева СО РАН

FWNF-2024-0001

In the previous paper by the authors Linke et al. Mathematics. — V.12(12). 1890 (2024), for a wide class of nonparametric regression models, new kerneltype estimators belonging to the class of local linear ones were proposed. The kernel estimators from Linke et al. Mathematics. — V.12(12). 1890 (2024) are universal with respect to design constraints that ensure uniform consistency of this new estimators. In Linke et al. Mathematics. — V.12(12). 1890 (2024), all that is required is an asymptotically dense filling of the domain of the regression function with design elements when the sample size tends to infinity. This condition is essentially necessary to restore the regression function and includes the cases of both fixed design, at the same time, without the requirement of its regularity, and random one, and not necessarily consisting of independent or weakly dependent random variables. In the present paper, the results from Linke et al. Mathematics. — V.12(12). 1890 (2024) are illustrated by computer modeling and examples of processing real numerical data from the field of medicine and are compared with several other estimation approaches. In all the numerical examples, the new universal local linear estimators exhibited robust performance, in contrast to certain common models which occasionally showed inflated errors.

Linke Y.Y. , Borisov I.S. , Ruzankin P.S. , Kutsenko V.A. , Yarovaya E.B. , Shalnova S.A.
Multivariate Universal Local Linear Kernel Estimators in Nonparametric Regression: Simulations and Real Data Processing
Sankhya A. 2025. P.1-28. DOI: 10.1007/s13171-025-00391-z WOS Scopus РИНЦ OpenAlex

Поступила в редакцию:	26 янв. 2025 г.
Опубликована online:	16 мая 2025 г.

Web of science:	WOS:001489322000001
Scopus:	2-s2.0-105005092568
РИНЦ:	82336455
OpenAlex:	W4410452613

Пока нет цитирований