Consistency properties for the wavelet estimator in nonparametric regression model with dependent errors

AbstractIn this paper, we establish the pth mean consistency, complete consistency, and the rate of complete consistency for the wavelet estimator in a nonparametric regression model with m-extended negatively dependent random errors. We show that the best rates can be nearly $O(n^{-1/3})$ O ( n − 1 / 3 ) under some general conditions. The results obtained in the paper markedly improve and extend some corresponding ones to a much more general setting.

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Complete consistency for the estimator of nonparametric regression model based on m-END errors

Open Mathematics ◽

10.1515/math-2021-0081 ◽

2021 ◽

Vol 19 (1) ◽

pp. 1197-1209

Author(s):

Shui-Li Zhang ◽

Tiantian Hou ◽

Cong Qu

Keyword(s):

Regression Model ◽

Nonparametric Regression ◽

Convergence Rates ◽

Nonparametric Regression Model ◽

Complete Consistency ◽

Model Based ◽

General Conditions

Abstract In this paper, we study the complete consistency for the estimator of nonparametric regression model based on m-END errors and obtain the convergence rates of the complete consistency under more general conditions. Finally, some simulations are illustrated to verify the validity of our results.

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On Complete Consistency for the Estimator of Nonparametric Regression Model Based on Asymptotically Almost Negatively Associated Errors

Methodology And Computing In Applied Probability ◽

10.1007/s11009-020-09813-x ◽

2020 ◽

Author(s):

Aiting Shen ◽

Siyao Zhang

Keyword(s):

Regression Model ◽

Nonparametric Regression ◽

Nonparametric Regression Model ◽

Negatively Associated ◽

Complete Consistency ◽

Model Based ◽

Asymptotically Almost Negatively Associated

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

Communication in Statistics- Theory and Methods ◽

10.1080/03610926.2019.1635160 ◽

2019 ◽

pp. 1-13

Author(s):

Shuili Zhang ◽

Tiantian Hou ◽

Cong Qu

Keyword(s):

Regression Model ◽

Nonparametric Regression ◽

Martingale Difference ◽

Nonparametric Regression Model ◽

Complete Consistency ◽

Model Based

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A note on the consistency of wavelet estimators in nonparametric regression model under widely orthant dependent random errors

Mathematica Slovaca ◽

10.1515/ms-2017-0323 ◽

2019 ◽

Vol 69 (6) ◽

pp. 1471-1484

Author(s):

Liwang Ding ◽

Ping Chen

Keyword(s):

Numerical Simulation ◽

Regression Model ◽

Nonparametric Regression ◽

Random Variables ◽

Random Errors ◽

Nonparametric Regression Model ◽

Moment Conditions ◽

Widely Orthant Dependent ◽

The Moment ◽

Wavelet Estimators

Abstract In this paper, we consider the wavelet estimators of a nonparametric regression model based on widely orthant dependent random errors. The moment consistency and the completely consistency for wavelet estimators under some more mild moment conditions are investigated. The results obtained in the paper improve and extend the corresponding ones for dependent random variables. Finally, we provide a numerical simulation to verify the validity of our results.

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The Berry-Esseen bound of a wavelet estimator in non-randomly designed nonparametric regression model based on ANA errors

ESAIM Probability and Statistics ◽

10.1051/ps/2019017 ◽

2020 ◽

Vol 24 ◽

pp. 21-38

Author(s):

Xufei Tang ◽

Xuejun Wang ◽

Yi Wu ◽

Fei Zhang

Keyword(s):

Regression Model ◽

Numerical Simulations ◽

Nonparametric Regression ◽

Random Variables ◽

Nonparametric Regression Model ◽

Wavelet Estimator ◽

Negatively Associated ◽

Model Based

Consider the nonparametric regression model Yni = g(tni) + εi, i = 1, 2, …, n, n ≥ 1, where εi, 1 ≤ i ≤ n, are asymptotically negatively associated (ANA, for short) random variables. Under some appropriate conditions, the Berry-Esseen bound of the wavelet estimator of g(⋅) is established. In addition, some numerical simulations are provided in this paper. The results obtained in this paper generalize some corresponding ones in the literature.

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