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.

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.

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

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Qihui He ◽  
Mingming Chen
Keyword(s):  
Regression Model ◽  
Nonparametric Regression ◽  
General Setting ◽  
Random Errors ◽  
Nonparametric Regression Model ◽  
Wavelet Estimator ◽  
Complete Consistency ◽  
Consistency Properties ◽  
General Conditions

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.

Estimation of nonstationary nonparametric regression model with multiplicative structure

2021 ◽  
Author(s):  
Likai Chen ◽  
Ekaterina Smetanina ◽  
Wei Biao Wu
Keyword(s):  
Regression Model ◽  
Nonparametric Regression ◽  
Risk Premium ◽  
Convergence Rates ◽  
Broad Class ◽  
Estimation Procedure ◽  
Small Samples ◽  
Nonparametric Regression Model ◽  
Conditional Mean ◽  
Mean Function

Abstract This paper presents a multiplicative nonstationary nonparametric regression model which allows for a broad class of nonstationary processes. We propose a three-step estimation procedure to uncover the conditional mean function and establish uniform convergence rates and asymptotic normality of our estimators. The new model can also be seen as a dimension-reduction technique for a general two-dimensional time-varying nonparametric regression model, which is especially useful in small samples and for estimating explicitly multiplicative structural models. We consider two applications: estimating a pricing equation for the US aggregate economy to model consumption growth, and estimating the shape of the monthly risk premium for S&P 500 Index data.

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