A Beta-Based Heteroskedasticity-Consistent Covariance Matrix Estimator

Abstract

This paper introduces an adaptive framework for leverage correction in heteroskedasticity-consistent covariance matrix estimation for ordinary least squares regression. Unlike existing heteroskedasticity-consistent estimators, which rely on predetermined leverage adjustment functions, the proposed approach introduces an adaptive leverage correction calibrated to the empirical leverage structure of the design matrix. It replaces the conventional leverage-based adjustment used in existing heteroskedasticity-consistent estimators with a data-driven correction derived from a fitted Beta distribution. The Beta parameters are estimated from the observed leverage values, allowing the adjustment factors to adapt automatically to the leverage structure of the sample. By exploiting information from the entire leverage configuration rather than from individual leverage values alone, the proposed estimator accommodates heterogeneous leverage patterns while avoiding the excessive growth of adjustment factors that may arise with some existing methods. Monte Carlo simulations show that the proposed estimator yields accurate finite-sample inference and confidence interval coverage while retaining the desired asymptotic properties. Empirical applications further illustrate its practical advantages in the presence of influential observations, particularly in situations where existing estimators exhibit overshooting of leverage adjustment factors. To facilitate its adoption, an open-source R package, hcinfer, has been developed and made publicly available.