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Optimizing effective numbers of tests by vine copula modeling

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  • Steffen Nico

    (University of Bremen, Institute for Statistics)

  • Dickhaus Thorsten

    (University of Bremen, Institute for Statistics)

Abstract

In the multiple testing context, we utilize vine copulae for optimizing the effective number of tests. It is well known that for the calibration of multiple tests for control of the family-wise error rate the dependencies between the marginal tests are of utmost importance. It has been shown in previous work, that positive dependencies between the marginal tests can be exploited in order to derive a relaxed Šidák-type multiplicity correction. This correction can conveniently be expressed by calculating the corresponding „effective number of tests“ for a given (global) significance level. This methodology can also be applied to blocks of test statistics so that the effective number of tests can be calculated by the sum of the effective numbers of tests for each block. In the present work, we demonstrate how the power of the multiple test can be optimized by taking blocks with high inner-block dependencies. The determination of those blocks will be performed by means of an estimated vine copula model. An algorithm is presented which uses the information of the estimated vine copula to make a data-driven choice of appropriate blocks in terms of (estimated) dependencies. Numerical experiments demonstrate the usefulness of the proposed approach.

Suggested Citation

  • Steffen Nico & Dickhaus Thorsten, 2020. "Optimizing effective numbers of tests by vine copula modeling," Dependence Modeling, De Gruyter, vol. 8(1), pages 172-185, January.
    • Handle: RePEc:vrs:demode:v:8:y:2020:i:1:p:172-185:n:10
    DOI: 10.1515/demo-2020-0010
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    References listed on IDEAS

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    1. 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.
    2. Müller, Alfred & Scarsini, Marco, 2005. "Archimedean copulæ and positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 434-445, April.
    3. 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.
    4. Dißmann, J. & Brechmann, E.C. & Czado, C. & Kurowicka, D., 2013. "Selecting and estimating regular vine copulae and application to financial returns," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 52-69.
    5. Nagler, T. & Bumann, C. & Czado, C., 2019. "Model selection in sparse high-dimensional vine copula models with an application to portfolio risk," Journal of Multivariate Analysis, Elsevier, vol. 172(C), pages 180-192.
    6. Dickhaus, Thorsten & Gierl, Jakob, 2012. "Simultaneous test procedures in terms of p-value copulae," SFB 649 Discussion Papers 2012-049, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
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