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Minimax test for fuzzy hypotheses

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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.

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Acknowledgements

The authors would like to thank the respected anonymous referees and Editor-in-Chief whose comments improved the paper.

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Authors and Affiliations

  1. Department of Statistics, Faculty of Mathematics and Computer, Shahid Bahonar University of Kerman, Kerman, Iran

    Abbas Parchami & Mashaallah Mashinchi

  2. Faculty of Engineering Science, College of Engineering, University of Tehran, Tehran, Iran

    S. Mahmoud Taheri

  3. Department of Statistics and Mathematical Methods in Economics, Faculty of Mathematics and Geoinformation, Vienna University of Technology, Wiedner Hauptstraße 8-10, 1040, Wien, Austria

    Reinhard Viertl

Authors
  1. Abbas Parchami
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  2. S. Mahmoud Taheri
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  3. Reinhard Viertl
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  4. Mashaallah Mashinchi
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Correspondence to S. Mahmoud Taheri.

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Parchami, A., Taheri, S.M., Viertl, R. et al. Minimax test for fuzzy hypotheses. Stat Papers 59, 1623–1648 (2018). https://doi.org/10.1007/s00362-017-0926-4

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  • DOI: https://doi.org/10.1007/s00362-017-0926-4

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