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Asymptotic and Bootstrap techniques for testing the expected value of a fuzzy random variable

Author

Listed:
  • Manuel Montenegro
  • Ana Colubi
  • María Rosa Casals
  • María Ángeles Gil

Abstract

In this paper we will consider hypothesis-tests for the (fuzzy-valued) mean value of a fuzzy random variable in a population. For this purpose, we will make use of a generalized metric for fuzzy numbers, and we will develop an approach for normal fuzzy random variables, and two different approaches for the case of fuzzy random variables taking on a finite number of different values. A real-life example illustrates the use of the last two approaches. Finally, a comparison between the introduced techniques is developed by means of simulation studies leading to close inferential conclusions. Copyright Springer-Verlag 2004

Suggested Citation

  • Manuel Montenegro & Ana Colubi & María Rosa Casals & María Ángeles Gil, 2004. "Asymptotic and Bootstrap techniques for testing the expected value of a fuzzy random variable," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 59(1), pages 31-49, February.
    • Handle: RePEc:spr:metrik:v:59:y:2004:i:1:p:31-49
    DOI: 10.1007/s001840300270
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    Citations

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    Cited by:

    1. Renato Coppi & Paolo Giordani & Pierpaolo D’Urso, 2006. "Component Models for Fuzzy Data," Psychometrika, Springer;The Psychometric Society, vol. 71(4), pages 733-761, December.
    2. Alfred Mbairadjim Moussa & Jules Sadefo Kamdem, 2022. "A fuzzy multifactor asset pricing model," Annals of Operations Research, Springer, vol. 313(2), pages 1221-1241, June.
    3. Gil, Maria Angeles & Montenegro, Manuel & Gonzalez-Rodriguez, Gil & Colubi, Ana & Rosa Casals, Maria, 2006. "Bootstrap approach to the multi-sample test of means with imprecise data," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 148-162, November.
    4. Nather, Wolfgang, 2006. "Regression with fuzzy random data," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 235-252, November.
    5. Abbas Parchami & Przemyslaw Grzegorzewski & Maciej Romaniuk, 2024. "Statistical simulations with LR random fuzzy numbers," Statistical Papers, Springer, vol. 65(6), pages 3583-3600, August.
    6. Nguyen, Hung T. & Wu, Berlin, 2006. "Random and fuzzy sets in coarse data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 70-85, November.
    7. Colubi, Ana & Gonzalez-Rodriguez, Gil, 2007. "Triangular fuzzification of random variables and power of distribution tests: Empirical discussion," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4742-4750, May.
    8. Choirat, Christine & Seri, Raffaello, 2014. "Bootstrap confidence sets for the Aumann mean of a random closed set," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 803-817.
    9. González-Rodríguez, Gil & Colubi, Ana & Gil, María Ángeles, 2012. "Fuzzy data treated as functional data: A one-way ANOVA test approach," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 943-955.
    10. María Casals & Norberto Corral & María Gil & María López & María Lubiano & Manuel Montenegro & Gloria Naval & Antonia Salas, 2013. "Bertoluzza et al.’s metric as a basis for analyzing fuzzy data," METRON, Springer;Sapienza Università di Roma, vol. 71(3), pages 307-322, November.
    11. Ana Ramos-Guajardo & Ana Colubi & Gil González-Rodríguez & María Gil, 2010. "One-sample tests for a generalized Fréchet variance of a fuzzy random variable," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(2), pages 185-202, March.
    12. Coppi, Renato & Gil, Maria A. & Kiers, Henk A.L., 2006. "The fuzzy approach to statistical analysis," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 1-14, November.
    13. Lubiano, María Asunción & Montenegro, Manuel & Sinova, Beatriz & de la Rosa de Sáa, Sara & Gil, María Ángeles, 2016. "Hypothesis testing for means in connection with fuzzy rating scale-based data: algorithms and applications," European Journal of Operational Research, Elsevier, vol. 251(3), pages 918-929.
    14. Gonzalez-Rodriguez, Gil & Colubi, Ana & Angeles Gil, Maria, 2006. "A fuzzy representation of random variables: An operational tool in exploratory analysis and hypothesis testing," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 163-176, November.

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