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

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: nonlinearity 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 nonlinear model is considered. The studied estimators combine weighted $$MM-$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>M</mml:mi> <mml:mi>M</mml:mi> <mml:mo>-</mml:mo> </mml:mrow> </mml:math> regression estimators, to control the impact of high leverage points, and a robust method to estimate the parameters of the variance function.