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• W2122478484 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 ℳd(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 challenging concrete 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 nonasymptotic regions with controlled coverage are limited to the binomial case d=2. Here we propose a new method valid for any d≥2 that provides confidence regions with controlled coverage and small volume. The method involves 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." @default.
• W2122478484 created "2016-06-24" @default.
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• W2122478484 date "2009-09-01" @default.
• W2122478484 modified "2023-10-16" @default.
• W2122478484 title "Confidence Regions for the Multinomial Parameter With Small Sample Size" @default.
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• W2122478484 doi "https://doi.org/10.1198/jasa.2009.tm08152" @default.
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