Estimation of the Variance Function in Heteroscedastic Linear Regression Models

Abstract

Heteroscedasticity generally exists when a linear regression model is applied to analyzing some real-world problems. Therefore, how to accurately estimate the variance functions of the error term in a heteroscedastic linear regression model is of great importance for obtaining efficient estimates of the regression parameters and making valid statistical inferences. A method for estimating the variance function of heteroscedastic linear regression models is proposed in this article based on the variance-reduced local linear smoothing technique. Some simulations and comparisons with other method are conducted to assess the performance of the proposed method. The results demonstrate that the proposed method can accurately estimate the variance functions and therefore produce more efficient estimates of the regression parameters.

Keywords:

• Generalized least-squares
• Heteroscedastic linear regression model
• Nonparametric regression model
• Variance-reduced local linear smoothing technique

Mathematics Subject Classification:

• Primary 62J05
• Secondary 62G05

Acknowledgment

This research was supported by the National Science Foundation of China (No. 10531030).