EM-Test for Finite Mixture Models

• Activity Number: 459
• Type: Topic Contributed
• Date/Time: Wednesday, August 4, 2010 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Jiahua Chen*+ and Pengfei Li
• Companies: The University of British Columbia and University of Alberta
• Keywords: finite mixture model ; hypothesis test ; chisquare bar distribution

Abstract

Designing a valid and easy-to-use statistical test for the order of the finite mixture model is challenging. Most results on hypothesis tests to date have focused on a special case of homogeneity. Some general results are limited to theoretical interest and difficult to implement. In this talk, we apply an EM-test for the null hypothesis of order $m_0$ versus an alternative hypothesis of order larger than $m_0$. The null limiting distribution of the proposed EM-test is found to be a mixture of $chi^2$ distributions. The weights in this mixture limiting distribution when $m_0 = 1, 2, 3$ have simple forms and can be conveniently estimated. Simulation study indicates the limiting distribution is a good approximation to the finite sample distributions and the test has good efficiency.