Order selection in finite mixture models: complete or observed likelihood information criteria?
成果类型：
Article
署名作者：
Hui, Francis K. C.; Warton, David I.; Foster, Scott D.
署名单位：
University of New South Wales Sydney; Commonwealth Scientific & Industrial Research Organisation (CSIRO)
刊物名称：
BIOMETRIKA
ISSN/ISSBN：
0006-3444
DOI：
10.1093/biomet/asv027
发表日期：
2015
页码：
724730
关键词：
摘要：
Choosing the number of components in a finite mixture model is a challenging task. In this article, we study the behaviour of information criteria for selecting the mixture order, based on either the observed likelihood or the complete likelihood including component labels. We propose a new observed likelihood criterion called aic(mix), which is shown to be order consistent. We further show that when there is a nontrivial level of classification uncertainty in the true model, complete likelihood criteria asymptotically underestimate the true number of components. A simulation study illustrates the potentially poor finite-sample performance of complete likelihood criteria, while aic(mix) and the Bayesian information criterion perform strongly regardless of the level of classification uncertainty.