Robust estimation of heteroscedastic regression models: a brief overview and new proposals

TL;DR

This paper reviews robust methods for heteroscedastic nonlinear regression models, addressing challenges posed by non-linearity, heteroscedasticity, and outliers, and proposes new iterative estimation procedures combining weighted MM-estimators and variance function estimation.

Contribution

It provides a comprehensive overview of existing robust approaches and introduces new iterative procedures for more reliable parameter estimation in heteroscedastic nonlinear models.

Findings

Enhanced robustness against outliers and high leverage points.

Improved estimation accuracy in heteroscedastic nonlinear models.

Effective handling of combined non-linearity and heteroscedasticity.

Abstract

We collect robust proposals given in the field of regression models with heteroscedastic errors. Our motivation stems from the fact that the practitioner frequently faces the confluence of two phenomena in the context of data analysis: non--linearity and heteroscedasticity. The impact of heteroscedasticity on the precision of the estimators is well--known, however the conjunction of these two phenomena makes handling outliers more difficult. An iterative procedure to estimate the parameters of a heteroscedastic non--linear model is considered. The studied estimators combine weighted $MM-$regression estimators, to control the impact of high leverage points, and a robust method to estimate the parameters of the variance function.