Revisiting consistency of a recursive estimator of mixing distributions

Abstract

Estimation of the mixing distribution under a general mixture model is a very difficult problem, especially when the mixing distribution is assumed to have a density. Predictive recursion (PR) is a fast, recursive algorithm for nonparametric estimation of a mixing distribution/density in general mixture models. However, the existing PR consistency results make rather strong assumptions, some of which fail for practically relevant mixture models. In this paper, we first develop new consistency results for PR under weaker conditions and then we apply this theory in the important case of mixtures of scaled uniform kernels.