A note on the efficiency of sandwich covariance matrix estimation
A note on the efficiency of sandwich covariance matrix estimation
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DOI：
10.1198/016214501753382309
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发表时间：
2001-12-01
影响因子：
3.7
通讯作者：
Carroll, RJ
中科院分区：
文献类型：
--
作者：
Kauermann, G;Carroll, RJ
三明治估计量，也被称为稳健协方差矩阵估计量、异方差一致协方差矩阵估计量或经验协方差矩阵估计量，随着广义估计方程的日益普及，在计量经济学文献中得到了越来越多的应用。它的优点是，即使当拟合的参数模型不成立或甚至没有指定时，它也为参数估计提供了协方差矩阵的一致估计。令人惊讶的是你。我们对拟似然模型中的三明治估计量进行了渐近的研究，对线性情况下的三明治估计量进行了解析的研究。我们表明，在准似然模型正确的情况下，三明治估计往往比通常的参数方差估计具有更大的变数，增加的方差是该方法的一个固定特征，也是即使参数模型失败或存在异方差时也要获得一致性所付出的代价。我们表明，额外的可变性直接影响由三明治方差估计构建的置信区间的覆盖概率。事实上，使用三明治方差估计与t分布分位数相结合，给出了覆盖概率低于标称值的置信区间。我们建议进行调整以弥补这一事实。
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 thou.-h, 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.