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Nonparametric Archimedean generator estimation with implications for multiple testing

Author

Listed:
  • André Neumann

    (University of Bremen)

  • Thorsten Dickhaus

    (University of Bremen)

Abstract

In multiple testing, the family-wise error rate can be bounded under some conditions by the copula of the test statistics. Assuming that this copula is Archimedean, we consider two nonparametric Archimedean generator estimators. More specifically, we use the nonparametric estimator from Genest et al. (Test 20(2):223–256, 2011) and a slight modification thereof. In simulations, we compare the resulting multiple tests with the Bonferroni test and the multiple test derived from the true generator as baselines.

Suggested Citation

  • André Neumann & Thorsten Dickhaus, 2020. "Nonparametric Archimedean generator estimation with implications for multiple testing," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(2), pages 309-323, June.
    • Handle: RePEc:spr:alstar:v:104:y:2020:i:2:d:10.1007_s10182-020-00363-8
    DOI: 10.1007/s10182-020-00363-8
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    References listed on IDEAS

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    1. Müller, Alfred & Scarsini, Marco, 2005. "Archimedean copulæ and positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 434-445, April.
    2. Jens Stange & Taras Bodnar & Thorsten Dickhaus, 2015. "Uncertainty quantification for the family-wise error rate in multivariate copula models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 99(3), pages 281-310, July.
    3. Wolfgang Härdle & Ostap Okhrin, 2010. "De copulis non est disputandum," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 94(1), pages 1-31, March.
    4. Barbe, Philippe & Genest, Christian & Ghoudi, Kilani & Rémillard, Bruno, 1996. "On Kendall's Process," Journal of Multivariate Analysis, Elsevier, vol. 58(2), pages 197-229, August.
    5. René Schmidt & Andreas Faldum & Joachim Gerß, 2015. "Adaptive designs with arbitrary dependence structure based on Fisher’s combination test," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(3), pages 427-447, September.
    6. Christian Genest & Johanna Nešlehová & Johanna Ziegel, 2011. "Inference in multivariate Archimedean copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 223-256, August.
    7. Thorsten Dickhaus & Jakob Gierl, 2012. "Simultaneous test procedures in terms of p-value copulae," SFB 649 Discussion Papers SFB649DP2012-049, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    8. Christian Genest & Johanna Nešlehová & Johanna Ziegel, 2011. "Rejoinder on: Inference in multivariate Archimedean copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 290-292, August.
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