AI 中文总结
该研究针对普通最小二乘回归，提出用基于贝塔分布的数据驱动校正取代传统杠杆率调整来估计异方差一致协方差矩阵，经模拟和实证验证其优势，还开发了开源R包，能准确推断并适应异质杠杆率模式。
AI 中文摘要
本文为普通最小二乘回归引入了一种新的异方差一致协方差矩阵估计器。该估计器用基于拟合贝塔分布的数据驱动校正取代了现有异方差一致估计器中使用的传统基于杠杆率的调整。贝塔参数从观测到的杠杆率值估计得出，使调整因子能自动适应样本的杠杆率结构。由此，该估计器能适应异质杠杆率模式，避免一些现有方法中调整因子过度增长。蒙特卡罗模拟表明，该估计器能产生准确的有限样本推断和置信区间覆盖，同时保留所需的渐近性质。实证应用进一步说明了其在存在有影响观测值时的实际优势。为便于采用，还开发并公开了一个开源R包hcinfer。
英文摘要
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.
