Abstract #301307

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JSM 2003 Abstract #301307
Activity Number: 447
Type: Contributed
Date/Time: Thursday, August 7, 2003 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract - #301307
Title: Fuzzy Confidence Intervals and P Values
Author(s): Charles J. Geyer*+ and Glen D. Meeden
Companies: University of Minnesota and University of Minnesota
Address: 270 Vincent Hall, Minneapolis, MN, 55455-0488,
Keywords: P value ; hypothesis test ; fuzzy set theory ; randomized test ; uniformly most powerful unbiased ; confidence interval
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 optimality of UMP and UMPU tests. The analogous concept for P values, called fuzzy P values, also inherits the same optimality.

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