Testing Homogeneity for Non-Negative Distributions with a Clump of Zeros

• Activity Number: 27
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
• Sponsor: SSC
• Author(s): Chunlin Wang*+ and Yukun Liu and Pengfei Li and Paul K. Marriott
• Companies: University of Waterloo and East China Normal University and University of Waterloo and University of Waterloo
• Keywords: density ratio model ; empirical likelihood ; multinomial logistic regression ; point-mass mixture model

Abstract

The problem of assessing homogeneity among multiple non-negative samples with possibly excessive zero observations arises naturally in many applications. A unique feature associated with several such populations is that: each group of the data consist a mixture of zero mass and a continuous component whose distribution is usually highly skewed. Therefore, the existing nonparametric methods are inefficient to detect the differences while the fully parametric methods are sensitive to the underlying assumptions. In this talk, we propose a new empirical likelihood ratio (ELR) test under the semiparametric density ratio model. The test is generically applicable to a broad family of parametric distributions with possibly heavy zeros. We further develop a bootstrap version of the proposed test to improve the control of type I error which in some cases may be inflated. The bootstrap ELR test yields a more accurate estimate of size and offers competitive and robust power under a wide range of alternatives. We study asymptotic properties of the proposed ELR test and demonstrate its performance via simulation studies and real-data analysis.