Non-parametric identification and estimation of the number of components in multivariate mixtures

• 成果类型: Article
• 署名作者: Kasahara, Hiroyuki; Shimotsu, Katsumi
• 署名单位: University of British Columbia; University of Tokyo
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12022
• 发表日期: 2014
• 页码: 97-111
• 关键词: latent structure models; finite mixture; CONSISTENT ESTIMATION; tests; inference

摘要

We analyse the identifiability of the number of components in k-variate, M-component finite mixture models in which each component distribution has independent marginals, including models in latent class analysis. Without making parametric assumptions on the component distributions, we investigate how one can identify the number of components from the distribution function of the observed data. When k2, a lower bound on the number of components (M) is non-parametrically identifiable from the rank of a matrix constructed from the distribution function of the observed variables. Building on this identification condition, we develop a procedure to estimate a lower bound on the number of components consistently.