A Minimax Bias Estimator for OLS Variances under Heteroskedasticity

TL;DR

This paper derives new analytic formulas for the bias of heteroskedasticity-consistent covariance estimators in linear regression, introducing a minimax bias estimator that outperforms the standard Eicker-White method.

Contribution

It provides the first explicit bias formulas for a class of heteroskedasticity-consistent estimators and proposes a new minimax bias estimator with improved performance.

Findings

New bias formulas for heteroskedasticity-consistent covariance estimators

A minimax bias estimator that reduces maximum bias

Substantial improvement over the Eicker-White estimator

Abstract

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.