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Minimax test for fuzzy hypotheses

Author

Listed:
  • Abbas Parchami

    (Shahid Bahonar University of Kerman)

  • S. Mahmoud Taheri

    () (University of Tehran)

  • Reinhard Viertl

    (Vienna University of Technology)

  • Mashaallah Mashinchi

    (Shahid Bahonar University of Kerman)

Abstract

Abstract In hypotheses testing, such as other statistical problems, we may confront imprecise concepts. One case is a situation in which the hypotheses of interest are imprecise. In this paper, we recall and redefine some concepts about testing fuzzy hypotheses and then we provide a minimax approach to the problem of testing fuzzy hypotheses by using crisp (non-fuzzy) data. We give some illustrative/numerical examples, by which we study the effect of fuzziness by using the power functions of minimax tests.

Suggested Citation

  • Abbas Parchami & S. Mahmoud Taheri & Reinhard Viertl & Mashaallah Mashinchi, 2018. "Minimax test for fuzzy hypotheses," Statistical Papers, Springer, vol. 59(4), pages 1623-1648, December.
  • Handle: RePEc:spr:stpapr:v:59:y:2018:i:4:d:10.1007_s00362-017-0926-4
    DOI: 10.1007/s00362-017-0926-4
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    References listed on IDEAS

    as
    1. Abbas Parchami & S. Taheri & Mashaallah Mashinchi, 2012. "Testing fuzzy hypotheses based on vague observations: a p-value approach," Statistical Papers, Springer, vol. 53(2), pages 469-484, May.
    2. Abbas Parchami & S. Taheri & Mashaallah Mashinchi, 2010. "Fuzzy p-value in testing fuzzy hypotheses with crisp data," Statistical Papers, Springer, vol. 51(1), pages 209-226, January.
    3. Bernhard Arnold, 1996. "An approach to fuzzy hypothesis testing," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 44(1), pages 119-126, December.
    4. S. Taheri & G. Hesamian, 2013. "A generalization of the Wilcoxon signed-rank test and its applications," Statistical Papers, Springer, vol. 54(2), pages 457-470, May.
    5. P. Filzmoser & R. Viertl, 2004. "Testing hypotheses with fuzzy data: The fuzzy p-value," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(1), pages 21-29, February.
    6. Casals, M. R. & Gil, M. A. & Gil, P., 1986. "The fuzzy decision problem: An approach to the problem of testing statistical hypotheses with fuzzy information," European Journal of Operational Research, Elsevier, vol. 27(3), pages 371-382, December.
    7. Hamzeh Torabi & Javad Behboodian, 2007. "Likelihood ratio tests for fuzzy hypotheses testing," Statistical Papers, Springer, vol. 48(3), pages 509-522, September.
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