Adaptive Estimation of Heteroscedastic Linear Regression Models Using Heteroscedasticity Consistent Covariance Matrix

Abstract

For the estimation of linear regression models in the presence of heteroscedasticity of unknown form, method of ordinary least squares does not provide the estimates with the smallest variances. In this situation, adaptive estimators are used, namely, nonparametric kernel estimator and nearest neighbour regression estimator. But these estimators rely on substantially restrictive conditions. In order to have accurate inferences in the presence of heteroscedasticity of unknown form, it is a usual practice to use heteroscedasticity consistent covariance matrix (HCCME). Following the idea behind the construction of HCCME, we formulate a new estimator. The Monte Carlo results show the encouraging performance of the proposed estimator in the sense of efficiency while comparing it with the available adaptive estimators especially in small samples that makes it more attractive in practical situations.