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K-sample tests for equality of variances of random fuzzy sets

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  • Ramos-Guajardo, Ana Belén
  • Lubiano, María Asunción

Abstract

The problem of testing equality of variances often arises when distributions of random variables are compared or linear models between them are considered. The usual tests for variances given normality of the underlying populations are highly non-robust to non-normality and are strongly dependent on the kurtosis. Some alternative formulations of Levene’s test statistic for testing the homoscedasticity have been shown to be powerful and robust under non-normality. On the basis of Levene’s classical procedure, a test for the equality of variances of k fuzzy-valued random elements is developed. Accordingly, consistent asymptotic and bootstrap tests are established and their empirical behaviour is analyzed by means of extensive simulation studies. In addition, the proposed test is compared with a Bartlett-type test. A case-study illustrating the applicability of the procedure is presented.

Suggested Citation

  • Ramos-Guajardo, Ana Belén & Lubiano, María Asunción, 2012. "K-sample tests for equality of variances of random fuzzy sets," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 956-966.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:4:p:956-966
    DOI: 10.1016/j.csda.2010.11.025
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    References listed on IDEAS

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    2. 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.
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    7. 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.
    8. 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.
    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.
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    Cited by:

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    2. Colubi, Ana & Ramos-Guajardo, Ana Belén, 2023. "Fuzzy sets and (fuzzy) random sets in Econometrics and Statistics," Econometrics and Statistics, Elsevier, vol. 26(C), pages 84-98.
    3. Coletti, Giulianella & Gervasi, Osvaldo & Tasso, Sergio & Vantaggi, Barbara, 2012. "Generalized Bayesian inference in a fuzzy context: From theory to a virtual reality application," Computational Statistics & Data Analysis, Elsevier, vol. 56(4), pages 967-980.
    4. 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.
    5. Pierpaolo D’Urso & María Ángeles Gil, 2017. "Fuzzy data analysis and classification," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 11(4), pages 645-657, December.

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