Open Access
November 2005 Fuzzy and Randomized Confidence Intervals and P-Values
Charles J. Geyer, Glen D. Meeden
Statist. Sci. 20(4): 358-366 (November 2005). DOI: 10.1214/088342305000000340


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.


Download Citation

Charles J. Geyer. Glen D. Meeden. "Fuzzy and Randomized Confidence Intervals and P-Values." Statist. Sci. 20 (4) 358 - 366, November 2005.


Published: November 2005
First available in Project Euclid: 12 January 2006

zbMATH: 1130.62319
MathSciNet: MR2210225
Digital Object Identifier: 10.1214/088342305000000340

Keywords: Confidence interval , fuzzy set theory , hypothesis test , p-value , randomized test , uniformly most powerful unbiased (UMP and UMPU)

Rights: Copyright © 2005 Institute of Mathematical Statistics

Vol.20 • No. 4 • November 2005
Back to Top