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Performance comparison of variance models in a robust estimation method for heteroscedastic nonlinear models
Journal of the Korean Data & Information Science Society 2021;32:243-56
Published online January 31, 2021;  https://doi.org/10.7465/jkdi.2021.32.1.243
© 2021 Korean Data and Information Science Society.

Yiehwa Lee1 · Changwon Lim2

12Department of Applied statistics, Chung-Ang University
Correspondence to: 1Master graduation, Department of Applied Statistics, Chung-Ang University, 84, Heukseok-ro, Dongjak-gu, Seoul 06974, Korea.
2Corresponding author: Professor, Department of Applied Statistics, Chung-Ang University, 84, Heukseok-ro, Dongjak-gu, Seoul 06974, Korea. E-mail: clim@cau.ac.kr
Received October 19, 2020; Revised November 23, 2020; Accepted November 27, 2020.
This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (http://creativecommons.org/licenses/by-nc/3.0) which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Nonlinear regression models are commonly used in various fields such as toxicology/pharmacology. When analyzing data using a nonlinear regression model the structure of error variance plays a key role in the estimation of parameters. Particularly, when data do not satisfy the homoscedasticity assumption, it is important to use an appropriate estimation method. In this paper, a robust M-estimation method against potential outliers in nonlinear regression under heteroscedasticity is considered. Under the heteroscedasticity assumption, three variance models are considered, and a weighted M-estimator is studied by the simulation to compare the performance of the estimator with three variance models. From the results of the simulation studies, even though not as well as proper estimators, WME using a nonlinear variance model generally shows good performances for homoscedastic data and heteroscedastic data with the variance models. The methods are also illustrated by analyzing real toxicological data.
Keywords : Dose-response study, heteroscedasticity, nonlinear regression model, variance model, weighted M-estimation.