Local M-estimation for Conditional Variance in Heteroscedastic Regression Models

In this article, we develop a local M-estimation for the conditional variance in heteroscedastic regression models. The estimator is based on the local linear smoothing technique and the M-estimation technique, and it is shown to be not only asymptotically equivalent to the local linear estimator but also robust. The consistency and asymptotic normality of the local M-estimator for the conditional variance in heteroscedastic regression models are obtained under mild conditions. The simulation studies demonstrate that the proposed estimators perform well in robustness.