Recursive nonparametric predictive for a discrete regression model

Abstract

A recursive algorithm is proposed to estimate a set of distribution functions indexed by a regressor variable. The procedure is fully nonparametric and has a Bayesian motivation and interpretation. Indeed, the recursive algorithm follows a certain Bayesian update, defined by the predictive distribution of a Dirichlet process mixture of linear regression models. Consistency of the algorithm is demonstrated under mild assumptions, and numerical accuracy in finite samples is shown via simulations and real data examples. The algorithm is very fast to implement, it is parallelizable, sequential, and requires limited computing power.