Universal local linear kernel estimators in nonparametric regression

TL;DR

This paper introduces new local linear kernel estimators for nonparametric regression that are uniformly consistent under broad conditions, including dependent and irregular design data, with applications to functional data and real medical datasets.

Contribution

The paper develops a class of local linear estimators that do not require classical independence or regularity conditions, broadening applicability in nonparametric regression.

Findings

Estimators are uniformly consistent under dependent and irregular designs.

Simulations demonstrate estimator performance.

Application to real medical data shows practical effectiveness.

Abstract

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 depen\-dence 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.