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Exact confidence intervals and hypothesis tests for parameters of discrete distributions
Uppsala University, Disciplinary Domain of Humanities and Social Sciences, Faculty of Social Sciences, Department of Statistics.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Applied Mathematics and Statistics.
2017 (English)In: Bernoulli, ISSN 1350-7265, E-ISSN 1573-9759, Vol. 23, no 1, 479-502 p.Article in journal (Refereed) Published
Abstract [en]

We study exact confidence intervals and two-sided hypothesis tests for univariate parameters of stochastically increasing discrete distributions, such as the binomial and Poisson distributions. It is shown that several popular methods for constructing short intervals lack strict nestedness, meaning that accepting a lower confidence level not always will lead to a shorter confidence interval. These intervals correspond to a class of tests that are shown to assign differing p-values to indistinguishable models. Finally, we show that among strictly nested intervals, fiducial intervals, including the Clopper-Pearson interval for a binomial proportion and the Garwood interval for a Poisson mean, are optimal.

Place, publisher, year, edition, pages
2017. Vol. 23, no 1, 479-502 p.
Keyword [en]
binomial distribution, confidence interval, expected length, fiducial interval, hypothesis test, Poisson distribution
National Category
Probability Theory and Statistics
Identifiers
URN: urn:nbn:se:uu:diva-229398DOI: 10.3150/15-BEJ750ISI: 000389565500017OAI: oai:DiVA.org:uu-229398DiVA: diva2:736451
Available from: 2014-08-06 Created: 2014-08-06 Last updated: 2017-12-05Bibliographically approved

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Thulin, MånsZwanzig, Silvelyn

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