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

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.

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

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.

scholarly journals On adaptivity of wavelet thresholding estimators with negatively super-additive dependent noise

2019 ◽  
Vol 69 (6) ◽  
pp. 1485-1500 ◽  
Author(s):  
Yuncai Yu ◽  
Xinsheng Liu ◽  
Ling Liu ◽  
Weisi Liu
Keyword(s):  
Regression Model ◽  
Numerical Simulations ◽  
Nonparametric Regression ◽  
Besov Spaces ◽  
Convergence Rates ◽  
Wavelet Thresholding ◽  
Nonparametric Regression Model ◽  
Optimal Convergence ◽  
Optimal Convergence Rates ◽  
Block Thresholding

Abstract This paper considers the nonparametric regression model with negatively super-additive dependent (NSD) noise and investigates the convergence rates of thresholding estimators. It is shown that the term-by-term thresholding estimator achieves nearly optimal and the block thresholding estimator attains optimal (or nearly optimal) convergence rates over Besov spaces. Additionally, some numerical simulations are implemented to substantiate the validity and adaptivity of the thresholding estimators with the presence of NSD noise.

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

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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