Non-finite Fisher information and homogeneity: an EM approach

• 成果类型: Article
• 署名作者: Li, P.; Chen, J.; Marriott, P.
• 署名单位: University of Alberta; University of British Columbia; University of Waterloo
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asp011
• 发表日期: 2009
• 页码: 411426
• 关键词: likelihood-ratio test; local mixture-models; genetic-linkage; asymptotics; tests

摘要

Even simple examples of finite mixture models can fail to fulfil the regularity conditions that are routinely assumed in standard parametric inference problems. Many methods have been investigated for testing for homogeneity in finite mixture models, for example, but all rely on regularity conditions including the finiteness of the Fisher information and the space of the mixing parameter being a compact subset of some Euclidean space. Very simple examples where such assumptions fail include mixtures of two geometric distributions and two exponential distributions, and, more generally, mixture models in scale distribution families. To overcome these difficulties, we propose and study an em-test statistic, which has a simple limiting distribution for examples in this paper. Simulations show that the em-test has accurate Type I errors and is more efficient than existing methods when they are applicable. A real example is included.