The Annals of Statistics

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

D. Dacunha-Castelle and E. Gassiat

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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.

Article information

Ann. Statist. Volume 27, Number 4 (1999), 1178-1209.

First available in Project Euclid: 4 April 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62F05: Asymptotic properties of tests
Secondary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20]

Model selection tests nonidentifiable models mixtures ARMA processes


Dacunha-Castelle, D.; Gassiat, E. Testing the order of a model using locally conic parametrization: population mixtures and stationary ARMA processes. Ann. Statist. 27 (1999), no. 4, 1178--1209. doi:10.1214/aos/1017938921.

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