A Conditional Score Test for Homogeneity in Generalized Semiparametric Exponential Family Mixture Models

• Activity Number: 577 - Semiparametric Modeling in Biometric Data
• Type: Contributed
• Date/Time: Wednesday, August 2, 2017 : 2:00 PM to 3:50 PM
• Sponsor: Biometrics Section
• Author(s): Rui Duan* and Yang Ning and Bruce George Lindsay and Yong Chen
• Companies: University of Pennsylvania and Cornell University and The Pennsylvania State University, Department of Statistics and University of Pennsylvania
• Keywords: Exponential tilt model ; Composite likelihood ; Homogeneity test ; Mixture model ; Nonregular model ; Semiparametric model

Abstract

In biomedical studies, testing for homogeneity between two groups where one group is modeled by parametric mixture models is often of interest. In this study, we use a semiparametric exponential family mixture model where the distribution function for the reference group is unspecified. By allowing Box-Cox transformations, the model extends the exponential family mixture model and offers more flexibility to characterize the heterogeneity. We construct a novel score test to test the homogeneity between two groups. To address the technical challenges due to irregularities of the mixture model, we propose a modification of the score test, so that the resulting test enjoys the Wilks phenomenon. We show the finite-sample most powerful property and asymptotic power function of the proposed test. The proposed test is evaluated by simulation studies and applied to a DNA methylation data set.