Bootstrapping MM-estimators for linear regression with fixed designs

Abstract

In this paper, I study the extension of the robust bootstrap [Salibian-Barrera, M., Zamar, R.H., 2002. Bootstrapping robust estimates of regression. Ann. Statist. 30, 556–582] to the case of fixed designs. The robust bootstrap is a computer-intensive inference method for robust regression estimators which is computationally simple (because we do not need to re-compute the robust estimate with each bootstrap sample) and robust to the presence of outliers in the bootstrap samples. In this paper, I prove the consistency of this method for the case of non-random explanatory variables and illustrate its use on a real data set. Simulation results indicate that confidence intervals based on the robust bootstrap have good finite-sample coverage levels.