Homogeneity Testing Under Finite Location-Scale Mixtures

• Activity Number: 69 - Highlights of the Canadian Journal of Statistics
• Type: Invited
• Date/Time: Monday, August 9, 2021 : 10:00 AM to 11:50 AM
• Sponsor: SSC (Statistical Society of Canada)
• Author(s): Jiahua Chen* and Pengfei Li and Guangfu Liu
• Companies: University of British Columbia and University of Waterloo and Shanghai University of International Business and Economic
• Keywords: Computer experiments; EM-test; limiting distribution; location-scale family; mixture models; tuning parameter

Abstract

The testing problem for the order of finite mixture models has a long history and remains an active research topic. Since Ghosh (1985) revealed the hard-to-manage asymptotic properties of the likelihood ratio test, many successful alternative approaches have been developed. The most successful attempts include the modified likelihood ratio test and the EM-test, which lead to neat solutions for finite mixtures of univariate normal distributions, finite mixtures of single-parameter distributions, and several mixture-like models. The problem remains challenging, and there is still no generic solution for location-scale mixtures. In this paper, we provide an EM-test solution for homogeneity for finite mixtures of location-scale family distributions. This EM-test has nonstandard limiting distributions, but we are able to find the critical values numerically. We use computer experiments to obtain appropriate values for the tuning parameters. A simulation study shows that the fine-tuned EM-test has close to nominal type I errors and very good power properties. Two application examples are included to demonstrate the performance of the EM-test.