Universal Local Linear Kernel Estimators in Nonparametric Regression

被引：11

作者：

Linke, Yuliana ^{[1
]}

Borisov, Igor ^{[1
]}

Ruzankin, Pavel ^{[1
]}

Kutsenko, Vladimir ^{[2
,3
]}

Yarovaya, Elena ^{[2
,3
]}

Shalnova, Svetlana ^{[3
]}

机构：

[1] Sobolev Inst Math, Novosibirsk 630090, Russia

[2] Lomonosov Moscow State Univ, Dept Probabil Theory, Moscow 119234, Russia

[3] Natl Med Res Ctr Therapy & Prevent Med, Dept Epidemiol Noncommunicable Dis, Moscow 101990, Russia

来源：

MATHEMATICS | 2022年 / 10卷 / 15期

关键词：

nonparametric regression; kernel estimator; local linear estimator; uniform consistency; fixed design; random design; dependent design elements; mean of dense functional data; epidemiological research; UNIFORM-CONVERGENCE RATES; FUNCTIONAL DATA; ASYMPTOTIC PROPERTIES; FIXED-DESIGN; CONSISTENCY; SPARSE;

D O I：

10.3390/math10152693

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

New local linear estimators are proposed for a wide class of nonparametric regression models. The estimators are uniformly consistent regardless of satisfying traditional conditions of dependence of design elements. The estimators are the solutions of a specially weighted least-squares method. The design can be fixed or random and does not need to meet classical regularity or independence conditions. As an application, several estimators are constructed for the mean of dense functional data. The theoretical results of the study are illustrated by simulations. An example of processing real medical data from the epidemiological cross-sectional study ESSE-RF is included. We compare the new estimators with the estimators best known for such studies.

引用

页数：28