Model-robust regression and a Bayesian ``sandwich'' estimator

Details Model-robust regression and a Bayesian ``sandwich'' estimator Model-robust regression and a Bayesian ``sandwich'' estimator

2011-01-07

arxiv.org/abs/1101.1402v1

Annals of Applied Statistics 2010, Vol. 4, No. 4, 2099-2113

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Published in at http://dx.doi.org/10.1214/10-AOAS362 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Ins

Scientific paper

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.

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