scholarly journals Robust Estimation and Tests for Parameters of Some Nonlinear Regression Models

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 599
Author(s):  
Pengfei Liu ◽  
Mengchen Zhang ◽  
Ru Zhang ◽  
Qin Zhou
Keyword(s):  
Asymptotic Normality ◽  
Robust Estimation ◽  
Empirical Likelihood ◽  
Nonlinear Regression ◽  
Regression Models ◽  
Nonlinear Least Squares ◽  
Likelihood Method ◽  
Nonlinear Regression Models ◽  
Simulation Performance ◽  
Consistency And Asymptotic Normality

This paper uses the median-of-means (MOM) method to estimate the parameters of the nonlinear regression models and proves the consistency and asymptotic normality of the MOM estimator. Especially when there are outliers, the MOM estimator is more robust than nonlinear least squares (NLS) estimator and empirical likelihood (EL) estimator. On this basis, we propose hypothesis testing Statistics for the parameters of the nonlinear regression models using empirical likelihood method, and the simulation performance shows the superiority of MOM estimator. We apply the MOM method to analyze the top 50 data of GDP of China in 2019. The result shows that MOM method is more feasible than NLS estimator and EL estimator.

scholarly journals On the Whittle estimator for linear random noise spectral density parameter in continuous-time nonlinear regression models

2019 ◽  
Vol 23 (1) ◽  
pp. 129-169 ◽  
Author(s):  
A. V. Ivanov ◽  
N. N. Leonenko ◽  
I. V. Orlovskyi
Keyword(s):  
Spectral Density ◽  
Nonlinear Regression ◽  
Continuous Time ◽  
Regression Models ◽  
Random Noise ◽  
Sufficient Conditions ◽  
Density Parameter ◽  
Noise Spectral Density ◽  
Nonlinear Regression Models ◽  
Consistency And Asymptotic Normality

Abstract A continuous-time nonlinear regression model with Lévy-driven linear noise process is considered. Sufficient conditions of consistency and asymptotic normality of the Whittle estimator for the parameter of spectral density of the noise are obtained in the paper.

LEAST SQUARES ESTIMATION FOR NONLINEAR REGRESSION MODELS WITH HETEROSCEDASTICITY

2021 ◽  
pp. 1-23
Author(s):  
Qiying Wang
Keyword(s):  
Least Squares ◽  
Nonlinear Regression ◽  
Regression Models ◽  
Asymptotic Theory ◽  
Nonlinear Least Squares ◽  
Least Squares Estimation ◽  
Nonlinear Regression Models ◽  
Nonlinear Least Squares Estimation ◽  
New Framework

This paper develops an asymptotic theory of nonlinear least squares estimation by establishing a new framework that can be easily applied to various nonlinear regression models with heteroscedasticity. As an illustration, we explore an application of the framework to nonlinear regression models with nonstationarity and heteroscedasticity. In addition to these main results, this paper provides a maximum inequality for a class of martingales, which is of interest in its own right.

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