Hellinger Deviance Testing for Mixture Complexity

• Activity Number: 24
• Type: Topic Contributed
• Date/Time: Sunday, August 1, 2010 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): An-Lin Cheng*+ and Anand Vidyashankar
• Companies: University of Missouri-Kansas City and George Mason University
• Keywords: Hellinger deviance test ; mixture model ; Robust estimation

Abstract

In a mixture model with k components and a kernel distribution from a one-parameter family, we consider robust testing of the hypothesis H0 : k = 2 against the alternative H1 : k > 2. We describe a penalized Hellinger deviance test and derive its asymptotic limit distribution under the null hypothesis. Robustness of the method is evaluated using the theoretical behavior of Type I error rates. Extensive simulations using Normal, Poisson, Binomial and Gamma models show that the methodology works well in practice. Finally, our work also shows that the proposed methodology outperforms, in terms of robustness, other existing methods in the literature.