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On Weak Convergence of the Bootstrap Copula Empirical Process with Random Resample Size

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  • Salim Bouzebda

    (LMAC (Laboratory of Applied Mathematics of Compiègne), Université de Technologie de Compiègne, 60200 Compiègne, France)

Abstract

The purpose of this note is to provide a description of the weak convergence of the random resample size bootstrap empirical process. The principal results are used to estimate the sample rank correlation coefficients using Spearman’s and Kendall’s respective methods. In addition to this, we discuss how our findings can be applied to statistical testing.

Suggested Citation

  • Salim Bouzebda, 2023. "On Weak Convergence of the Bootstrap Copula Empirical Process with Random Resample Size," Stats, MDPI, vol. 6(1), pages 1-16, February.
    • Handle: RePEc:gam:jstats:v:6:y:2023:i:1:p:23-380:d:1077238
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    References listed on IDEAS

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    1. Christian Genest & Johanna Nešlehová & Noomen Ben Ghorbal, 2010. "Spearman's footrule and Gini's gamma: a review with complements," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(8), pages 937-954.
    2. Rémillard, Bruno & Scaillet, Olivier, 2009. "Testing for equality between two copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 377-386, March.
    3. Segers, Johan, 2012. "Asymptotics of empirical copula processes under non-restrictive smoothness assumptions," LIDAM Reprints ISBA 2012009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Schmid, Friedrich & Schmidt, Rafael, 2007. "Multivariate extensions of Spearman's rho and related statistics," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 407-416, February.
    5. Bouzebda, Salim, 2017. "Kac’s representation for empirical copula process from an asymptotic viewpoint," Statistics & Probability Letters, Elsevier, vol. 123(C), pages 107-113.
    6. Olivier Scaillet, 2005. "A Kolmogorov-Smirnov Type Test for Positive Quadrant Dependence," FAME Research Paper Series rp128, International Center for Financial Asset Management and Engineering.
    7. Soukarieh, Inass & Bouzebda, Salim, 2023. "Renewal type bootstrap for increasing degree U-process of a Markov chain," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    8. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    9. Inass Soukarieh & Salim Bouzebda, 2022. "Exchangeably Weighted Bootstraps of General Markov U -Process," Mathematics, MDPI, vol. 10(20), pages 1-42, October.
    10. Javad Behboodian & Ali Dolati & Manuel Úbeda-Flores, 2007. "A multivariate version of Gini's rank association coefficient," Statistical Papers, Springer, vol. 48(2), pages 295-304, April.
    11. Friedrich Schmid & Rafael Schmidt, 2007. "Nonparametric inference on multivariate versions of Blomqvist’s beta and related measures of tail dependence," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 66(3), pages 323-354, November.
    12. Jordan, Adriana & Ivanoff, B. Gail, 2013. "Multidimensional p–p plots and precedence tests for point processes on ℜd," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 122-137.
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