f-divergence estimation and two-sample homogeneity test under semiparametric density-ratio models

Details f-divergence estimation and two-sample homogeneity test under semiparametric density-ratio models f-divergence estimation and two-sample homogeneity test under semiparametric density-ratio models

2010-10-24

arxiv.org/abs/1010.4945v1

Statistics

Machine Learning

28 pages, 3 tables

Scientific paper

A density ratio is defined by the ratio of two probability densities. We study the inference problem of density ratios and apply a semi-parametric density-ratio estimator to the two-sample homogeneity test. In the proposed test procedure, the f-divergence between two probability densities is estimated using a density-ratio estimator. The f-divergence estimator is then exploited for the two-sample homogeneity test. We derive the optimal estimator of f-divergence in the sense of the asymptotic variance, and then investigate the relation between the proposed test procedure and the existing score test based on empirical likelihood estimator. Through numerical studies, we illustrate the adequacy of the asymptotic theory for finite-sample inference.

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