Dual-Likelihood Ratio Test for Type-I Censored Multiple Samples Under Semiparametric Density Ratio Models

• Activity Number: 240
• Type: Contributed
• Date/Time: Monday, August 5, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Song Cai*+ and Jiahua Chen
• Companies: University of British Columbia and Universithy of British Columbia
• Keywords: density ratio model ; emprical likelihood ; censoring ; semiparametric

Abstract

Density ratio model (DRM) is a flexible semiparametric model for the relationships among the densities of the underlying distributions of multiple samples. Empirical likelihood (EL) is a powerful tool for the inference of the DRM parameters. This paper establish EL theory for the inference of DRM parameters when the observations are type--I censored, e.g. the experiment stopped at a pre--specified level. We show that the maximum empirical likelihood estimator of the DRM parameter is identical to a maximum partial dual--empirical likelihood estimator. We also show that the corresponding dual--likelihood ratio statistic has a simple Chisquared limiting distribution under a class of general composite null hypothesis about the DRM parameters. This result is especially useful for testing the equality of entire underlying distributions of many different independent samples with type--I censored observations.