Fuzzy and randomized confidence intervals and p-values. (English) Zbl 1130.62319
Summary: 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.
MSC:
| 62F25 | Parametric tolerance and confidence regions |
| 62F03 | Parametric hypothesis testing |
| 62F99 | Parametric inference |
Keywords:
P-value; hypothesis test; uniformly most powerful unbiased (UMP and UMPU); fuzzy set theory; randomized testReferences:
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