University of Minnesota, Twin Cities School of Statistics
Title: Fuzzy and Randomized Confidence Intervals and P-values
Authors: Charles J. Geyer and Glen D. Meeden
Affiliation: School of Statistics, University of Minnesota
Abstract: 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, called fuzzy P-values or abstract randomized P-values, that also inherits the same exactness and optimality.
Key words and phrases: Confidence interval, P-value, hypothesis test, uniformly most powerful unbiased (UMP and UMPU), fuzzy set theory, randomized test.
Complete text of the current version of the paper as PostScript or as PDF.
The design document for the R package contains some mathematical arguments that were cut from the second version of the paper for reasons of length. It is available as PDF in the R package.
For purely historical reasons, earlier versions of the paper are still available
They contain nothing of interest that is not also in either the current version or the design document for the R package, except that the second version contains two figures cut from the third.