The Sandwich (robust Covariance Matrix) Estimator

The sandwich estimator, often known as the robust covariance matrix estimator or the empirical covariance matrix estimator, has achieved increasing use 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 a parametric model fails to hold, or is not even specified. Surprisingly though, there has been little discussion of the properties of the sandwich method other than consistency. We investigate the sandwich estimator in quasilikelihood models asymptotically, and in the linear case analytically. We show that when the quasilikelihood model is correct, the sandwich covariance matrix estimate is often far more variable than the usual parametric variance estimate, and its coverage probabilities can be abysmal. The increased variance is a fixed feature of the method, and the price one pays to obtain consistency even when the parametric model fails. We make some simple suggestions for modifying the method which improve coverage probabilities.