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

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...

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Bibliographic Details
Published inMathematics (Basel) Vol. 12; no. 12; p. 1890
Main Authors Linke, Yuliana, Borisov, Igor, Ruzankin, Pavel, Kutsenko, Vladimir, Yarovaya, Elena, Shalnova, Svetlana
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.06.2024
Subjects
Analysis
Dependent variables
Estimation theory
Estimators
fixed design
Kernel functions
Linear systems
local linear estimator
Methods
Multivariate analysis
nonparametric regression
Nonparametric statistics
random design
Random variables
Regression analysis
Regression models
strongly dependent design elements
uniform consistency
Russia
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12121890