Performance comparison of variance models in a robust estimation method for heteroscedastic nonlinear models

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.