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On empirical likelihood for semiparametric two-sample density ratio models
Authors:Amor Keziou  Samuela Leoni-Aubin
Affiliation:1. Laboratoire de Mathématiques (UMR 6056) CNRS, Université de Reims and LSTA, Université Paris 6, UFR Sciences, Moulin de la Housse, B.P. 1039, 51687 Reims, France;2. Université de Technologie de Compiègne, Centre de Recherche de Royallieu, Rue Personne de Roberval - BP 20529, 60205 Compiègne, France
Abstract:
We consider estimation and test problems for some semiparametric two-sample density ratio models. The profile empirical likelihood (EL) poses an irregularity problem 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 φφ-divergences and duality techniques. The asymptotic properties of the test statistic are presented both under the null and the alternative hypotheses, and approximation of the power function of the test is deduced.
Keywords:Biased two samples problem   Logistic regression   Case-control data   Test of homogeneity   Power function   Empirical likelihood   φ  si2.gif"   overflow="  scroll"  >φ-Divergences   Duality
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