Complete consistency for the estimator of nonparametric regression model based on martingale difference errors

Zhang, Shuili; Hou, Tiantian; Qu, Cong

doi:10.1080/03610926.2019.1635160

Cited by 6 publications

(1 citation statement)

References 21 publications

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“…In a number of recent studies, a more general condition max i≤n (X i − X i−1 ) → 0 can be found (e.g., see Yang and Yang, 2016;He, 2019;Wu et al, 2020). In several works, including those dealing with the so-called weighted estimators, certain conditions are imposed on the behavior of functions of design elements, but meaningful corresponding examples are limited to cases of regular design (e.g., see Zhang et al, 2019 ;Liang and Jing, 2005;Roussas et al, 1992;Georgiev, 1988).…”

Section: Introductionmentioning

confidence: 99%

Universal Local Linear Kernel Estimators in Nonparametric Regression

et al. 2022

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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.

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