The published version of this paper in Annals of Applied Statistics (Vol. 4, No. 4 (2010), 2099–2113) is available from the journal web site at http://dx.doi.org/10.1214/10-AOAS362.
We present a new Bayesian approach to model-robust linear regression that leads to uncertainty estimates with the same robustness properties as the Huber-White sandwich estimator. The sandwich estimator is known to provide asymptotically correct frequentist inference, even when standard modeling assumptions such as linearity and homoscedasticity in the data-generating mechanism are violated. Our derivation provides a compelling Bayesian justiﬁcation for using this simple and popular tool, and it also clariﬁes what is being estimated when the data-generating mechanism is not linear. We demonstrate the applicability of our approach using a simulation study and health care cost data from an evaluation of the Washington State Basic Health Plan.
Statistical Methodology | Statistical Theory
Szpiro, Adam A.; Rice, Kenneth M.; and Lumley, Thomas, "Model-Robust Regression and a Bayesian `Sandwich' Estimator" (May 2010). UW Biostatistics Working Paper Series. Working Paper 338.