Fuzzy and randomized confidence intervals and p-values. (English) Zbl 1130.62319

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.


62F25 Parametric tolerance and confidence regions
62F03 Parametric hypothesis testing
62F99 Parametric inference


ump; R
Full Text: DOI Euclid


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