Test of homogeneity in semiparametric two-sample density ratio models

We consider estimation and test problems for some sentiparametric two-sample density ratio models. The profile empirical likelihood (EL) poses an irregularity problern under the null hypothesis that the laws of the two samples are equal. We show that a 'dual' form of the profile EL is well defined even under the null hypothesis. A statistical test, based on the dual form of the EL ratio statistic (ELRS), is then proposed. We give an interpretation for the dual form of the ELRS through phi-divergences and 'duality' technique. The asymptotic properties of the test statistic are presented both under the null and the alternative hypotheses, and an approximation to the power function is deduced. (c) 2005 Academie des sciences. Published by Elsevier SAS. All rights reserved.