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Bootstrap confidence sets for the Aumann mean of a random closed set

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  • Choirat, Christine
  • Seri, Raffaello

Abstract

The objective is to develop a reliable method to build confidence sets for the Aumann mean of a random closed set as estimated through the Minkowski empirical mean. First, a general definition of the confidence set for the mean of a random set is provided. Then, a method using a characterization of the confidence set through the support function is proposed and a bootstrap algorithm is described, whose performance is investigated in Monte Carlo simulations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:803-817
    DOI: 10.1016/j.csda.2012.10.015
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    References listed on IDEAS

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    1. 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.
    2. Arie Beresteanu & Francesca Molinari, 2008. "Asymptotic Properties for a Class of Partially Identified Models," Econometrica, Econometric Society, vol. 76(4), pages 763-814, July.
    3. Hanna Jankowski & Larissa Stanberry, 2012. "Confidence Regions for Means of Random Sets Using Oriented Distance Functions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 39(2), pages 340-357, June.
    4. Cuevas, Antonio & Febrero, Manuel & Fraiman, Ricardo, 2006. "On the use of the bootstrap for estimating functions with functional data," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1063-1074, November.
    5. 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.
    6. 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.
    7. 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:

    1. 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.

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