Robust Estimation and Tests for Parameters of Some Nonlinear Regression Models

Pengfei Liu,Mengchen Zhang,Qin Zhou,Ru Zhang

doi:10.3390/math9060599

Pengfei Liu, Mengchen Zhang + Show 2 more

Open Access

https://doi.org/10.3390/math9060599

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Abstract

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.

Highlights

A nonlinear regression model refers to a regression model in which the relationship between variables is not linear
On the basis of the study of Zhang and Liu [8], this paper applies the MOM method to estimate the parameters of the nonlinear regression models and receives more robust results
We propose a new test method based on the empirical likelihood method

Summary

Introduction

A nonlinear regression model refers to a regression model in which the relationship between variables is not linear. Lecué and Lerasle [6] proposed new estimators for robust machine learning based on MOM estimators of the mean of real-valued random variables. These estimators achieved optimal rates of convergence under minimal assumptions on the dataset. Introduced the empirical likelihood (EL) estimator of the parameter of the nonlinear regression model based on the empirical likelihood method. On the basis of the study of Zhang and Liu [8], this paper applies the MOM method to estimate the parameters of the nonlinear regression models and receives more robust results. The paper is organized as follows: In Section 2, we review the definition of the nonlinear regression model and introduce the MOM method . A real application to GDP data is given in Section 5, and the conclusion is discussed in the last section

Median-of-Means Method Applies to Nonlinear Regression Model

Empirical Likelihood Test Based on MOM Method

Simulation Study

The Real Data Analysis

Findings

Conclusions