Divergence-type errors of smooth Barron-type density estimators

Abstract

Barron-type estimators are histogram-based distribution estimators that have been proved to have good consistency properties according to several information theoretic criteria. However they are not continuous. In this paper, we examine a new class of continuous distribution estimators obtained as a combination of Barron-type estimators with the frequency polygon. We prove the consistency of these estimators in expected information divergence and expected χ2-divergence. For one of then we evaluate the rate of convergence in expected χ2-divergence.