Robust regression via predictive recursion maximum likelihood

Robustness to specification of the error distribution is an important concern in regression. In this paper, we propose a general nonparametric scale mixture model for the error distribution. For fitting such mixtures, the predictive recursion method is a simple and computationally efficient alternative to existing methods. Here, a predictive recursion-based likelihood function is constructed, and estimation of the regression parameters proceeds by maximizing this function. A hybrid predictive recursion--EM algorithm is proposed for this purpose. The method's performance is compared with that of existing methods in simulations and real data analyses.