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August 1999 Testing the order of a model using locally conic parametrization: population mixtures and stationary ARMA processes
D. Dacunha-Castelle, E. Gassiat
Ann. Statist. 27(4): 1178-1209 (August 1999). DOI: 10.1214/aos/1017938921

Abstract

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.

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D. Dacunha-Castelle. E. Gassiat. "Testing the order of a model using locally conic parametrization: population mixtures and stationary ARMA processes." Ann. Statist. 27 (4) 1178 - 1209, August 1999. https://doi.org/10.1214/aos/1017938921

Information

Published: August 1999
First available in Project Euclid: 4 April 2002

zbMATH: 0957.62073
MathSciNet: MR1740115
Digital Object Identifier: 10.1214/aos/1017938921

Subjects:
Primary: 62F05
Secondary: 62H30

Rights: Copyright © 1999 Institute of Mathematical Statistics

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Vol.27 • No. 4 • August 1999
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