Efficient Estimation and Robust Inference of Linear Regression Models in the Presence of Heteroscedastic Errors and High Leverage Points

Abstract

It is common for linear regression models that the error variances are not the same for all observations and there are some high leverage data points. In such situations, the available literature advocates the use of heteroscedasticity consistent covariance matrix estimators (HCCME) for the testing of regression coefficients. Primarily, such estimators are based on the residuals derived from the ordinary least squares (OLS) estimator that itself can be seriously inefficient in the presence of heteroscedasticity. To get efficient estimation, many efficient estimators, namely the adaptive estimators are available but their performance has not been evaluated yet when the problem of heteroscedasticity is accompanied with the presence of high leverage data. In this article, the presence of high leverage data is taken into account to evaluate the performance of the adaptive estimator in terms of efficiency. Furthermore, our numerical work also evaluates the performance of the robust standard errors based on this efficient estimator in terms of interval estimation and null rejection rate (NRR).

Keywords:

• Adaptive estimator
• Adaptive heteroscedasticity-consistent interval estimator
• Estimated weighted least squares
• Heteroscedasticity consistent interval estimator
• Null rejection rate
• Size distortion

AMS Subject Classification:

• 62J05
• 62J86

Acknowledgments

We are very grateful to the anonymous referee for the thoughtful comments and suggestions to improve the earlier draft of this manuscript.