A Class of Pseudolikelihood Ratio Tests for Homogeneity in Exponential Tilt Mixture Models. (8th September 2014)

• Record Type: Journal Article
• Authors: Ning, Yang; Chen, Yong
• Is Part Of: Scandinavian journal of statistics. Volume 42:Number 2(2015:Jun.)
• Page Start: 504
• Page End: 517
• Publication Date: 2014-09-08
• Subjects: composite likelihood -- density ratio model -- non‐regular problem -- pairwise conditional likelihood; Statistics -- Periodicals; 310
• DOI: 10.1111/sjos.12119
• Languages: English
• ISSNs: 0303-6898

Abstract

Abstract: Mixture models are commonly used in biomedical research to account for possible heterogeneity in population. In this paper, we consider tests for homogeneity between two groups in the exponential tilt mixture models. A novel pairwise pseudolikelihood approach is proposed to eliminate the unknown nuisance function. We show that the corresponding pseudolikelihood ratio test has an asymptotic distribution as a supremum of two squared Gaussian processes under the null hypothesis. To maintain the appeal of simplicity for conventional likelihood ratio tests, we propose two alternative tests, both shown to have a simple asymptotic distribution of χ 1 2 under the null. Simulation studies show that the proposed class of pseudolikelihood ratio tests performs well in controlling type I errors and having competitive powers compared with the current tests. The proposed tests are illustrated by an example of partial differential expression detection using microarray data from prostate cancer patients.