## Statistical Science

### Fuzzy and Randomized Confidence Intervals and P-Values

#### 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 fuzzy P-values or abstract randomized P-values, that also inherits the same exactness and optimality.

#### Article information

Source
Statist. Sci., Volume 20, Number 4 (2005), 358-366.

Dates
First available in Project Euclid: 12 January 2006

https://projecteuclid.org/euclid.ss/1137076652

Digital Object Identifier
doi:10.1214/088342305000000340

Mathematical Reviews number (MathSciNet)
MR2210225

Zentralblatt MATH identifier
1130.62319

#### Citation

Geyer, Charles J.; Meeden, Glen D. Fuzzy and Randomized Confidence Intervals and P -Values. Statist. Sci. 20 (2005), no. 4, 358--366. doi:10.1214/088342305000000340. https://projecteuclid.org/euclid.ss/1137076652

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