A Minimax Bias Estimator for OLS Variances under Heteroskedasticity

Analytic evaluation of heteroskedasticity consistent covariance matrix estimates (HCCME) is difficult because of the complexity of the formulae currently available. We obtain new analytic formulae for the bias of a class of estimators of the covariance matrix of OLS in a standard linear regression model. These formulae provide substantial insight into the properties and performance characteristics of these estimators. In particular, we find a new estimator which minimizes the maximum possible bias and improves substantially on the standard Eicker-White estimate.