Homogeneity Test Under Finite Mixture with Multi-Dimensional Parameter Kernel

• Activity Number: 245 - Methods for Analysis of High-Dimensional Data
• Type: Contributed
• Date/Time: Monday, July 30, 2018 : 2:00 PM to 3:50 PM
• Sponsor: SSC
• Author(s): Ho Yin Ho* and Jiahua Chen
• Companies: University of British Columbia and University of British Columbia
• Keywords: finite mixture; test of homogeneity ; profile likelihood ratio; EM test

Abstract

Due to the irregularity features of finite mixture model, classic inference procedures are usually not directly applicable. Many testing procedures have been studied for testing for homogeneity though only a few of them are concerning mixture with multi-dimensional parameter kernel density. We develop a framework for testing homogeneity based on the profile Likelihood ratio. The proposed test statistic has a nice and simple asymptotic distribution, mixture of Chi squares. Penalties on mixing proportion and model parameters are introduced to control type I error while preserving the power. The result is applicable for mixture models with general multi-dimensional parameter kernel densities. Specifically, mixture of Gamma distribution and mixture of Logistic distribution are studied in detail. Simulations are conducted to assess the size and power of the test.