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Uncertainty quantification for the family-wise error rate in multivariate copula models

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  • Jens Stange
  • Taras Bodnar
  • Thorsten Dickhaus

Abstract

We derive confidence regions for the realized family-wise error rate (FWER) of certain multiple tests which are empirically calibrated at a given (global) level of significance. To this end, we regard the FWER as a derived parameter of a multivariate parametric copula model. It turns out that the resulting confidence regions are typically very much concentrated around the target FWER level, while generic multiple tests with fixed thresholds are in general not FWER-exhausting. Since FWER level exhaustion and optimization of power are equivalent for the classes of multiple test problems studied in this paper, the aforementioned findings militate strongly in favor of estimating the dependency structure (i.e., copula) and incorporating it in a multivariate multiple test procedure. We illustrate our theoretical results by considering two particular classes of multiple test problems of practical relevance in detail, namely multiple tests for components of a mean vector and multiple support tests. Copyright Springer-Verlag Berlin Heidelberg 2015

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  • 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.
    • Handle: RePEc:spr:alstar:v:99:y:2015:i:3:p:281-310
    DOI: 10.1007/s10182-014-0241-5
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    References listed on IDEAS

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    1. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    2. Taras Bodnar & Wolfgang Schmid, 2008. "A test for the weights of the global minimum variance portfolio in an elliptical model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(2), pages 127-143, March.
    3. Janssen, Paul & Swanepoel, Jan & Veraverbeke, Noël, 2014. "A note on the asymptotic behavior of the Bernstein estimator of the copula density," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 480-487.
    4. Diers, Dorothea & Eling, Martin & Marek, Sebastian D., 2012. "Dependence modeling in non-life insurance using the Bernstein copula," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 430-436.
    5. Sancetta, Alessio & Satchell, Stephen, 2004. "The Bernstein Copula And Its Applications To Modeling And Approximations Of Multivariate Distributions," Econometric Theory, Cambridge University Press, vol. 20(3), pages 535-562, June.
    6. Longin, Francois M., 2000. "From value at risk to stress testing: The extreme value approach," Journal of Banking & Finance, Elsevier, vol. 24(7), pages 1097-1130, July.
    7. Hofert, Marius & Mächler, Martin & McNeil, Alexander J., 2012. "Likelihood inference for Archimedean copulas in high dimensions under known margins," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 133-150.
    8. Joseph P. Romano & Michael Wolf, 2005. "Exact and Approximate Stepdown Methods for Multiple Hypothesis Testing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 94-108, March.
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    Cited by:

    1. Christina C. Bartenschlager & Jens O. Brunner, 2019. "Reaching for the stars: attention to multiple testing problems and method recommendations using simulation for business research," Journal of Business Economics, Springer, vol. 89(4), pages 447-479, June.
    2. Stange, Jens & Dickhaus, Thorsten & Navarro, Arcadi & Schunk, Daniel, 2016. "Multiplicity- and dependency-adjusted p-values for control of the family-wise error rate," Statistics & Probability Letters, Elsevier, vol. 111(C), pages 32-40.
    3. Carsten Bormann & Melanie Schienle, 2020. "Detecting Structural Differences in Tail Dependence of Financial Time Series," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 380-392, April.
    4. 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.
    5. 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.
    6. 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.

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