Heteroskedasticity-Consistent Covariance Matrix Estimators in Small Samples with High Leverage Points

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, th en remove them and recalculate the HCCMEs without these observations in order to c ompare 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 covariate s and disturbance term variances from the related literature in simulation r uns 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 leve rage (high MCD distance) observations had improved the HCCME performances consid erably and under some settings substantially, depending on the degree of leverage. We hope our theoretical findings will be benefited for practical purposes in applications.