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Confidence regions for the multinomial parameter with small sample size

Chafaï, D and Concordet, Didier Confidence regions for the multinomial parameter with small sample size. (2009) Journal of the American Statistical Association, vol. 1 (n° 487). pp. 1071-1079. ISSN 0162-1459

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Official URL: http://dx.doi.org/DOI:10.1198/jasa.2009.tm08152

Abstract

Consider the observation of n iid realizations of an experiment with d >= 2 possible outcomes, which corresponds to a single observation of a multinomial distribution M_d(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 >= 2. This method provides condence regions with controlled coverage and small volume, and consists in the inversion of the "cover- ing collection" associated to level-sets of the likelihood. The behavior when d=n tends to infinity remains an interesting open problem beyond the scope of this work.

Item Type:Article
Additional Information:Thanks to the American Statistical Association editor. The original PDF of the article can be found at the Journal of the American Statistical Association website : http://pubs.amstat.org/loi/jasa
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution: Université de Toulouse > Ecole Nationale Vétérinaire de Toulouse - ENVT
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Statistics:download
Deposited By:didier concordet

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