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 language | English (US) |
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Pages (from-to) | 358-366 |
Number of pages | 9 |
Journal | Statistical Science |
Volume | 20 |
Issue number | 4 |
DOIs | |
State | Published - Nov 2005 |
Keywords
- Confidence interval
- Fuzzy set theory
- Hypothesis test
- P-value
- Randomized test
- Uniformly most powerful unbiased (UMP and UMPU)