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

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.

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Estimation of nonstationary nonparametric regression model with multiplicative structure

Econometrics Journal ◽

10.1093/ectj/utab018 ◽

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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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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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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