Fuzzy and Randomized Confidence Intervals and P-Values

The optimal hypothesis tests for the binomial distribution and some other discrete distributions are uniformly most powerful (UMP) one-tailed and UMP unbiased (UMPU) two-tailed randomized tests. Conventional confidence intervals are not dual to randomized tests and perform badly on discrete data at...

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Bibliographic Details
Published in:Statistical science 2005-11, Vol.20 (4), p.358-366
Main Authors: Geyer, Charles J., Meeden, Glen D.
Format: Article
Language:English
Subjects:
Binomials
Confidence interval
Fuzzy set theory
Fuzzy sets
hypothesis test
Mathematical functions
Mathematical intervals
Membership functions
Null hypothesis
P values
P-value
randomized test
Sample size
uniformly most powerful unbiased (UMP and UMPU)
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Summary:The optimal hypothesis tests for the binomial distribution and some other discrete distributions are uniformly most powerful (UMP) one-tailed and UMP unbiased (UMPU) two-tailed randomized tests. Conventional confidence intervals are not dual to randomized tests and perform badly on discrete data at small and moderate sample sizes. We introduce a new confidence interval notion, called fuzzy confidence intervals, that is dual to and inherits the exactness and optimality of UMP and UMPU tests. We also introduce a new P-value notion, called fuzzy P-values or abstract randomized P-values, that also inherits the same exactness and optimality.
ISSN:0883-4237
2168-8745
DOI:10.1214/088342305000000340