The Annals of Applied Statistics

Model-robust regression and a Bayesian “sandwich” estimator

Adam A. Szpiro, Kenneth M. Rice, and Thomas Lumley

Full-text: Open access

Abstract

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.

Article information

Source
Ann. Appl. Stat., Volume 4, Number 4 (2010), 2099-2113.

Dates
First available in Project Euclid: 4 January 2011

Permanent link to this document
https://projecteuclid.org/euclid.aoas/1294167811

Digital Object Identifier
doi:10.1214/10-AOAS362

Mathematical Reviews number (MathSciNet)
MR2829948

Zentralblatt MATH identifier
1220.62025

Keywords
Bayesian inference estimating equations linear regression robust regression sandwich estimator

Citation

Szpiro, Adam A.; Rice, Kenneth M.; Lumley, Thomas. Model-robust regression and a Bayesian “sandwich” estimator. Ann. Appl. Stat. 4 (2010), no. 4, 2099--2113. doi:10.1214/10-AOAS362. https://projecteuclid.org/euclid.aoas/1294167811


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Supplemental materials

  • Supplementary material: Proofs of theorems in “Model robust regression and a Bayesian ‘sandwich’ estimator” (Szpiro, Rice, and Lumley). We provide proofs of the theorems stated in the paper “Model robust regression and a Bayesian ‘sandwich’ estimator” by Adam A. Szpiro, Kenneth M. Rice and Thomas Lumley.