A semiparametric scale-mixture regression model and predictive recursion maximum likelihood

To avoid specification of a particular distribution for the error in a regression model, we propose a flexible scale mixture model with a nonparametric mixing distribution. This model contains, among other things, the familiar normal and Student-t models as special cases. For fitting such mixtures, the predictive recursion method is a simple and computationally efficient alternative to existing methods. We define a predictive recursion-based marginal likelihood function, 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.