Robust Inference in the presence of Heteroscedasticity and High Leverage Points

Heteroscedasticity-consistent covariance matrixestimators are used as consistent estimates of variances of the parameters in linear regression. Different estimators known as HC0, HC3, HC4 and HC5 among others, were proposed in the literature as substitutes to the usual regression parameters' standard error, in order to alleviate the effect of the heteroscedastic variances. Although, most of these estimators were designed to also take care of the problem of high leverage points, nevertheless weighted version of these estimators were also proposed to further overcome the high leverage points. This article builds up from one existing weighted estimator, and proposed new weighting methods. We have tested their performance and found them useful on HC4 and HC5.