发表机构
Indiana University Bloomington（印第安纳大学布卢明顿分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文从投影几何视角提出结合聚类内与跨聚类残差矩的里斯方差估计量，解决传统HC、CRVE在回归投影非局部时低估抽样不确定性的问题，模拟及实证应用验证其有效性。
AI 中文摘要
线性回归的推断通常将普通最小二乘（OLS）残差作为未观测误差的代理变量。当回归投影相对于误差依赖结构是非局部的，该近似会失效。此时，残差化会在观测值和聚类间转移协方差信息，而传统的异方差一致（HC）估计量和聚类稳健方差估计量（CRVE）仅保留对角或聚类内残差矩，因此可能低估抽样不确定性。本文提出一种用于稳健方差估计的投影几何框架：OLS估计量的方差被精确表示为潜在协方差块的里斯（Riesz）泛函，可观测残差矩通过由完整回归投影决定的线性算子与目标关联，该公式将方差估计简化为线性逆问题。作者提出一种结合聚类内和跨聚类残差矩的里斯方差估计量，传统HC和CRVE是受限制的近似，其有效性取决于投影溢出可忽略；该估计量在聚类特定杠杆矩阵奇异时仍有良好定义，且通过避免显式矩阵求逆的迭代算法计算。模拟显示，在投影溢出下传统方法存在严重的覆盖率不足，而所提估计量恢复了接近名义水平的覆盖率；在殖民总督晋升的应用中，该修正改变了5个报告系数中4个的显著性。
英文摘要
Inference in linear regression commonly treats OLS residuals as proxies for unobserved errors. This approximation can fail when the regression projection is nonlocal relative to the error-dependence structure. Residualization then shifts covariance information across observations and clusters, while conventional heteroskedasticity-consistent (HC) and cluster-robust variance estimators (CRVE) retain only diagonal or within-cluster residual moments and may therefore understate sampling uncertainty. This paper develops a projection-geometry framework for robust variance estimation. The variance of the OLS estimator is represented exactly as a Riesz functional of latent covariance blocks, and observable residual moments are linked to the target through a linear operator determined by the full regression projection. This formulation reduces variance estimation to a linear inverse problem. I propose a Riesz variance estimator that combines within- and cross-cluster residual moments. Conventional HC and CRVE emerge as restricted approximations whose validity depends on negligible projection spillovers. The estimator remains well defined when cluster-specific leverage matrices are singular and is computed by an iterative algorithm that avoids explicit matrix inversion. Simulations show substantial undercoverage by conventional methods under projection spillovers, whereas the proposed estimator restores near-nominal coverage. In an application to colonial governor promotions, the correction changes the significance of four of five reported coefficients.
Comments79 pages. Accepted at North American Summer Meeting 2026
