The Sandwich Variance Estimator: Efficiency Properties and Coverage Probability of Confidence Intervals

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 the fitted 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. Under certain circumstances we show that when the quasilikelihood 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 one pays to obtain consistency even when the parametric model fails. 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 estimates combined with t-distribution quantiles gives confidence intervals with coverage probability falling below the nominal value. We propose a simple adjustment to compensate this defect, where the adjustment explicitly considers the variance of the sandwich estimate