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.