Work

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

Year: 2024

Type: article

Abstract: 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.

Source: Mathematics

DOI: 10.3390/math12121890

Authors: Yuliana Linke, Igor Borisov, Pavel Ruzankin, Vladimir Kutsenko, Elena Yarovaya, Svetlana Shalnova

Institutions: Novosibirsk State University, Sobolev Institute of Mathematics, Lomonosov Moscow State University, National Research Center for Preventive Medicine

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,955

OpenAlex ID: W4399809942

FWCI: 1.976

Cites: 77

Cited by: 6

Related to: 10