Fuzzy and randomized confidence intervals and P-values

Research output: Contribution to journalReview article

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Abstract

The optimal hypothesis tests for the binomial distribution and some other discrete distributions are uniformly most powerful (UMP) onetailed 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.

Original languageEnglish (US)
Pages (from-to)358-366
Number of pages9
JournalStatistical Science
Volume20
Issue number4
DOIs
StatePublished - Nov 1 2005

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Keywords

  • Confidence interval
  • Fuzzy set theory
  • Hypothesis test
  • P-value
  • Randomized test
  • Uniformly most powerful unbiased (UMP and UMPU)

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