Testing the order of a model using locally conic parametrization : population mixtures and stationary ARMA processes
Testing the order of a model using locally conic parametrization : population mixtures and stationary ARMA processes
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DOI：
10.1214/aos/1017938921
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发表时间：
1999-08
影响因子：
4.5
通讯作者：
D. Dacunha-Castelle;E. Gassiat
中科院分区：
文献类型：
--
作者：
D. Dacunha-Castelle;E. Gassiat
在本文中，我们解决的问题，使用似然比检验统计量在不可识别的模型，应用模型选择的情况下，参数化的较大的模型导致不可识别的较小的模型。我们给出了两个主要的应用程序：的情况下，人口的数量必须在一个混合物和平稳阿尔马（p，q）过程的情况下，顺序（p，q）进行测试。在检验模型的阶时，我们给出了似然比检验统计量的渐近分布。在ARMA的顺序选择的情况下，渐近分布是不变的参数生成的过程。局部二次曲线参数化是导出极限分布的关键工具，它允许人们发现两个问题之间的深层相似性。
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 be 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.