Divergence Estimation Using Density-Ratio and its Applications

Abstract

A density ratio is defined by the ratio of two probability densities, and it is widely applied to real world statistical problems. In this paper, we introduce moment matching estimators of density ratios and f-divergence estimators based on density-ratios. Then, we exploit the f-divergence estimators to the two-sample homogeneity test. We prove that the proposed test dominates the existing empirical likelihood score test. Through numerical studies, we illustrate the adequacy of the asymptotic theory for finite-sample inference.