Testing the order of a model using locally conic parametrization: Population mixtures and stationary ARMA processes

• 成果类型: Article
• 署名作者: Dacunha-Castelle, D; Gassiat, E
• 署名单位: Universite Paris Saclay
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1999
• 页码: 1178-1209
• 关键词: likelihood ratio

摘要

In this paper, we address the problem of testing hypotheses using the likelihood ratio test statistic in nonidentifiable models, with application to model selection in situations where the parametrization for the larger model leads to nonidentifiability in the smaller model. We give two major applications: the case where the number of populations has to be tested in a mixture and the case of stationary ARMA(p, q) processes where the order (p,q) has to he tested. We give the asymptotic distribution for the likelihood ratio test statistic when testing the order of the model. In the case of order selection for ARMAs, the asymptotic distribution is invariant with respect to the parameters generating the process. A locally conic parametrization is a key tool in deriving the limiting distributions; it allows one to discover the deep similarity between the two problems.