Testing the order of a model

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dc.creatorChambaz, Antoine
dc.date2006-07-31
dc.date.accessioned2026-07-07T08:08:03Z
dc.date.available2026-07-07T08:08:03Z
dc.descriptionThis paper deals with order identification for nested models in the i.i.d. framework. We study the asymptotic efficiency of two generalized likelihood ratio tests of the order. They are based on two estimators which are proved to be strongly consistent. A version of Stein's lemma yields an optimal underestimation error exponent. The lemma also implies that the overestimation error exponent is necessarily trivial. Our tests admit nontrivial underestimation error exponents. The optimal underestimation error exponent is achieved in some situations. The overestimation error can decay exponentially with respect to a positive power of the number of observations. These results are proved under mild assumptions by relating the underestimation (resp. overestimation) error to large (resp. moderate) deviations of the log-likelihood process. In particular, it is not necessary that the classical Cramér condition be satisfied; namely, the $\log$-densities are not required to admit every exponential moment. Three benchmark examples with specific difficulties (location mixture of normal distributions, abrupt changes and various regressions) are detailed so as to illustrate the generality of our results.
dc.descriptionPublished at http://dx.doi.org/10.1214/009053606000000344 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/math/0607806
dc.identifierhttp://arxiv.org/abs/math/0607806
dc.identifierAnnals of Statistics 2006, Vol. 34, No. 3, 1166-1203
dc.identifierdoi:10.1214/009053606000000344
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/131132
dc.subjectStatistics Theory
dc.subject60F10, 60G57, 62C99, 62F03, 62F05, 62F12 (Primary)
dc.titleTesting the order of a model
dc.typetext

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