Fuzzy and randomized confidence intervals and p-values. 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.

References in zbMATH (referenced in 27 articles , 1 standard article )

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  1. Akbari, Mohammad Ghasem; Hesamian, Gholamreza: Neyman-Pearson lemma based on intuitionistic fuzzy parameters (2019)
  2. Horváth, Lajos; Trapani, Lorenzo: Testing for randomness in a random coefficient autoregression model (2019)
  3. Rubin-Delanchy, Patrick; Heard, Nicholas A.; Lawson, Daniel J.: Meta-analysis of mid-(p)-values: some new results based on the convex order (2019)
  4. Vovk, Vladimir; Shen, Jieli; Manokhin, Valery; Xie, Min-ge: Nonparametric predictive distributions based on conformal prediction (2019)
  5. Hryniewicz, Olgierd: Statistical properties of the fuzzy (p)-value (2018)
  6. Hesamian, Gholamreza; Shams, Mehdi: Parametric testing statistical hypotheses for fuzzy random variables (2016)
  7. Habiger, Joshua D.: Multiple test functions and adjusted (p)-values for test statistics with discrete distributions (2015)
  8. Bamrungsetthapong, Wimonmas; Pongpullponsak, Adisak: Parameter interval estimation of system reliability for repairable multistate series-parallel system with fuzzy data (2014)
  9. Thulin, Måns: Coverage-adjusted confidence intervals for a binomial proportion (2014)
  10. Thulin, Måns: On split sample and randomized confidence intervals for binomial proportions (2014)
  11. Bodenhofer, Ulrich; Krone, Martin; Klawonn, Frank: Testing noisy numerical data for monotonic association (2013)
  12. Doebler, Anna; Doebler, Philipp; Holling, Heinz: Optimal and most exact confidence intervals for person parameters in item response theory models (2013)
  13. Bickel, David R.: The strength of statistical evidence for composite hypotheses: inference to the best explanation (2012)
  14. Parchami, Abbas; Taheri, S. Mahmoud; Mashinchi, Mashaallah: Testing fuzzy hypotheses based on vague observations: a (p)-value approach (2012)
  15. Piterbarg, Leonid I.: Parameter estimation from small biased samples: fuzzy sets vs statistics (2011)
  16. Terán, Pedro: Centrality as a gradual notion: a new bridge between fuzzy sets and statistics (2011)
  17. Thompson, Elizabeth: MCMC in the analysis of genetic data on related individuals (2011)
  18. Parchami, Abbas; Taheri, S. Mahmoud; Mashinchi, Mashaallah: Fuzzy (p)-value in testing fuzzy hypotheses with crisp data (2010)
  19. Geyer, Charles J.: Likelihood inference in exponential families and directions of recession (2009)
  20. Kulinskaya, Elena; Lewin, Alex: On fuzzy familywise error rate and false discovery rate procedures for discrete distributions (2009)

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