Inference on the Order of a Normal Mixture

• 成果类型: Article
• 署名作者: Chen, Jiahua; Li, Pengfei; Fu, Yuejiao
• 署名单位: University of British Columbia; University of Waterloo; York University - Canada
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2012.695668
• 发表日期: 2012
• 页码: 1096-1105
• 关键词: likelihood ratio test; gene-expression; number; components; homogeneity; selection; distance; models; tests

摘要

Finite normal mixture models are used in a wide range of applications. Hypothesis testing on the order of the normal mixture is an important yet unsolved problem. Existing procedures often lack a rigorous theoretical foundation. Many are also hard to implement numerically. In this article, we develop a new method to fill the void in this important area. An effective expectation-maximization (EM) test is invented for testing the null hypothesis of arbitrary order m(0) under a finite normal mixture model. For any positive integer m(0) >= 2, the limiting distribution of the proposed test statistic is chi(2)(2m0). We also use a novel computer experiment 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 provided. The procedure has been implemented in R code. The p-values for testing the null order of m(0) = 2 or m(0) = 3 can be calculated with a single command. This article has supplementary materials available online.