A Note on the Efficiency of Sandwich Covariance Matrix Estimation
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AI 根据所提供的论文材料归类：摘要研究通用协方差估计与区间覆盖，未明确涉及面板、因果推断等所列方向。
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夹心协方差矩阵估计效率的一则札记
- 研究问题
- 夹心协方差估计在模型失配时提供一致性的同时，当模型正确时会付出多大的额外变异代价，又如何影响置信区间覆盖？
- 方法与思路
- 作者对准似然模型进行渐近分析，并在线性情形开展解析研究，考察夹心方差估计的变异及使用 t 分位数构造区间的后果。
- 材料陈述的贡献
- 摘要称，某些条件下夹心估计比通常参数方差估计更易波动，额外变异导致区间覆盖低于名义水平；作者提出补偿调整。
- 阅读关注点
- 应核对额外变异出现的条件、比较采用的效率指标、区间覆盖分析和调整公式，以及模型正确与异方差情形的区别。
- 阅读边界
- 仅据版本未注明的 OpenAlex 索引摘要，无法确定调整形式和适用范围；不能将特定条件下的覆盖不足概括为所有稳健标准误。
原文摘要
The sandwich estimator, also known as robust covariance matrix estimator, heteroscedasticity-consistent covariance matrix estimate, or empirical covariance matrix estimator, has achieved increasing use in the econometric literature as well as with the growing popularity of generalized estimating equations. Its virtue is that it provides consistent estimates of the covariance matrix for parameter estimates even when the fitted parametric model fails to hold or is not even specified. Surprisingly though, there has been little discussion of properties of the sandwich method other than consistency. We investigate the sandwich estimator in quasi-likelihood models asymptotically, and in the linear case analytically. We show that under certain circumstances when the quasi-likelihood model is correct, the sandwich estimate is often far more variable than the usual parametric variance estimate. The increased variance is a fixed feature of the method and the price that one pays to obtain consistency even when the parametric model fails or when there is heteroscedasticity. We show that the additional variability directly affects the coverage probability of confidence intervals constructed from sandwich variance estimates. In fact, the use of sandwich variance estimates combined with t-distribution quantiles gives confidence intervals with coverage probability falling below the nominal value. We propose an adjustment to compensate for this fact.