scholarly journals The Bayesian Wavelet Thresholding Estimators of Nonparametric Regression Model Based on Mixture Prior Distribution

2021 ◽  
Vol 14 (2) ◽  
pp. 0-0
Author(s):  
Mahmood Afshari ◽  
Abouzar Bazyari ◽  
Yeganeh Moradian ◽  
Hamid Karamikabir ◽  
◽  
...  
Keyword(s):  
Regression Model ◽  
Nonparametric Regression ◽  
Prior Distribution ◽  
Wavelet Thresholding ◽  
Nonparametric Regression Model ◽  
Model Based ◽  
Mixture Prior ◽  
Bayesian Wavelet

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.

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 Complete Consistency of the Estimator of Nonparametric Regression Models Based onρ~-Mixing Sequences

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Xuejun Wang ◽  
Fengxi Xia ◽  
Meimei Ge ◽  
Shuhe Hu ◽  
Wenzhi Yang
Keyword(s):  
Regression Model ◽  
Nonparametric Regression ◽  
Regression Models ◽  
Nearest Neighbor ◽  
Type Inequality ◽  
Nonparametric Regression Model ◽  
Complete Consistency ◽  
Model Based ◽  
Rosenthal Type Inequality ◽  
Mixing Sequences

We study the complete consistency for estimator of nonparametric regression model based onρ~-mixing sequences by using the classical Rosenthal-type inequality and the truncated method. As an application, the complete consistency for the nearest neighbor estimator is obtained.

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