The Annals of Statistics
- Ann. Statist.
- Volume 27, Number 4 (1999), 1178-1209.
Testing the order of a model using locally conic parametrization: population mixtures and stationary ARMA processes
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.
Ann. Statist. Volume 27, Number 4 (1999), 1178-1209.
First available in Project Euclid: 4 April 2002
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 62F05: Asymptotic properties of tests
Secondary: 62H30: Classification and discrimination; cluster analysis [See also 68T10, 91C20]
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. https://projecteuclid.org/euclid.aos/1017938921