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| HAL : hal-00278790, version 3 |
| arXiv : 0805.1971 |
| DOI : 10.1198/jasa.2009.tm08152 |
| Fiche détaillée |  Récupérer au format |
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| Journal of the American Statistical Association 104, 487 (2009) 1071-1079 |
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| Versions disponibles : | v1 (14-05-2008) | v2 (14-05-2008) | v3 (12-12-2008) |
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| Confidence regions for the multinomial parameter with small sample size |
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Djalil Chafai 1, 2Didier Concordet 1, 2 |
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| (01/09/2009) |
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| Consider the observation of n iid realizations of an experiment with d>1 possible outcomes, which corresponds to a single observation of a multinomial distribution M(n,p) where p is an unknown discrete distribution on {1,...,d}. In many applications, the construction of a confidence region for p when n is small is crucial. This concrete challenging problem has a long history. It is well known that the confidence regions built from asymptotic statistics do not have good coverage when n is small. On the other hand, most available methods providing non-asymptotic regions with controlled coverage are limited to the binomial case d=2. In the present work, we propose a new method valid for any d>1. This method provides confidence regions with controlled coverage and small volume, and consists of the inversion of the "covering collection"' associated with level-sets of the likelihood. The behavior when d/n tends to infinity remains an interesting open problem beyond the scope of this work. |
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| 1 : | Physiopathologie et Toxicologie Expérimentales (UPTE) |
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INRA : UR0181 – Ecole Nationale Vétérinaire de Toulouse |
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| 2 : | Institut de Mathématiques de Toulouse (IMT) |
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Université Paul Sabatier - Toulouse III – Université Toulouse le Mirail - Toulouse II – Université des Sciences Sociales - Toulouse I – Institut National des Sciences Appliquées de Toulouse – CNRS : UMR5219 |
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| Domaine | : | Statistiques/Calcul |
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| Confidence regions – small samples – multinomial distribution |
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| Liste des fichiers attachés à ce document : | ||||||||||
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| hal-00278790, version 3 | |
| http://hal.archives-ouvertes.fr/hal-00278790 | |
| oai:hal.archives-ouvertes.fr:hal-00278790 | |
| Contributeur : Djalil Chafai | |
| Soumis le : Jeudi 11 Décembre 2008, 19:27:11 | |
| Dernière modification le : Mercredi 30 Septembre 2009, 17:02:03 | |
