Abstract
The aim of this paper is to demonstrate the impact of high leverage observations on the performances of prominent and popular Heteroskedasticity-Consistent Covariance Matrix Estimators (HCCMEs) with the help of computer simulation. Firstly, we figure out high leverage observations, then remove them and recalculate the HCCMEs without these observations in order to compare the HCCME performances with and without high leverage points. We identify high leverage observations with the Minimum Covariance Determinant (MCD). We select from among different covariates and disturbance term variances from the related literature in simulation runs in order to compare the percentage difference between the expected value of the HCCME and true covariance matrix as well as the symmetric loss function. Our results revealed that the elimination of high leverage (high MCD distance) observations had improved the HCCME performances considerably and under some settings substantially, depending on the degree of leverage. We hope our theoretical findings will be benefited for practical purposes in applications.
Highlights
An important assumption of the classical linear regression model is homoskedasticity, that is, the variances ofHow to cite this paper: Şimşek, E. and Orhan, M. (2016) Heteroskedasticity-Consistent Covariance Matrix Estimators in Small Samples with High Leverage Points
One way to cope with high leverage observations is to use the residuals by robust regression techniques. We suggest another approach to alleviate the negative effect of high leverage observations on Heteroskedasticity-Consistent Covariance Matrix Estimators (HCCMEs) performances
We suggest that detecting and removing high leverage points properly, improves the HCCME performances
Summary
An important assumption of the classical linear regression model is homoskedasticity, that is, the variances ofHow to cite this paper: Şimşek, E. and Orhan, M. (2016) Heteroskedasticity-Consistent Covariance Matrix Estimators in Small Samples with High Leverage Points. How to cite this paper: Şimşek, E. and Orhan, M. (2016) Heteroskedasticity-Consistent Covariance Matrix Estimators in Small Samples with High Leverage Points. The method of least squares is still used under heteroskedasticity, the covariance matrix estimators of the OLS coefficient estimates are not unbiased any more. That is why White (1980) [1] has made use of earlier studies by Eicker (1967) [2] to introduce his asymptotically unbiased Heteroskedasticity-Consistent Covariance Estimator (HCCME) for the covariance matrix in his influential 1980 Econometrica paper. This estimator is classified as biased in small samples (see [3])
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