Local M-estimation for Conditional Variance in Heteroscedastic Regression Models

Abstract

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.

Keywords:

• Conditional variance function
• Local M-estimator
• Local linear regression
• Nonlinear time series

Mathematics Subject Classification:

• 62G08
• 62G35