Inference on the Order of a Normal Mixture

• Activity Number: 323
• Type: Topic Contributed
• Date/Time: Tuesday, July 31, 2012 : 10:30 AM to 12:20 PM
• Sponsor: SSC
• Author(s): Yuejiao Fu*+ and Jiahua Chen and Pengfei Li
• Companies: York University and SSC and University of Waterloo
• Keywords: Normal Mixture models ; EM-test ; Likelihood ratio test ; Tuning parameter ; Unequal variance ; Chi-squared limiting distribution

Abstract

Finite normal mixture models are used in a wide range of applications. Determining the order of the mixture model is a vital step of the data analysis. Order selection procedures meet this need from one important angle. Yet when the order supports specific scientific propositions, an effective hypothesis test is indispensable. Existing hypothesis-test procedures for the order of the finite normal mixture often lack a rigorous theoretical foundation. Many are also hard to implement numerically. We develop a new method to fill the void in this important area. An effective EM-test is invented for testing the null hypothesis of arbitrary order m under a finite normal mixture model. For any positive integer m>=2, the proposed test statistic has a simple chi-squared limiting distribution. We also use a novel computer-experiment procedure to provide empirical formulas for the tuning parameter selection. The finite-sample performance of the test is examined through simulation studies. Real-data examples are also provided.