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Uniformly asymptotic normality of the weighted estimator in nonparametric regression model with φ-mixing errors

  • Chenlu Zhuansun , Gongxuan Zhang EMAIL logo and Kedong Yan
Published/Copyright: June 11, 2022
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Abstract

Consider the following nonparametric model: Yni=g(xni)+εni, 1 ⩽ i ⩽ n, where xniA are the nonrandom design points and A is a compact set of ℝm for some m=1, g (·) is a real valued function defined on A, and εn1, ⋅, εnn are zero mean φ-mixing random errors with finite moment of 2+δ order for some δ>0. Under some general conditions, we obtain the uniformly asymptotic normality of the weighted estimator of g (·). The rate of Berry-Esseen bound can approximate O(n−1/4) under some appropriate conditions. The validity of the main results is partially illustrated via a numerical simulation.

MSC 2010: Primary 60F15; 06D35
  1. (Communicated by Gejza Wimmer)

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Received: 2021-01-06
Accepted: 2021-05-04
Published Online: 2022-06-11
Published in Print: 2022-06-27

© 2022 Mathematical Institute Slovak Academy of Sciences

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