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Optimizing effective numbers of tests by vine copula modeling

Optimizing effective numbers of tests by vine copula modeling AbstractIn 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Dependence Modeling de Gruyter

Optimizing effective numbers of tests by vine copula modeling

Steffen, Nico; Dickhaus, Thorsten
Dependence Modeling , Volume 8 (1): 14 – Jan 1, 2020
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Publisher
de Gruyter
Copyright
© 2020 Nico Steffen et al., published by De Gruyter
ISSN
2300-2298
eISSN
2300-2298
DOI
10.1515/demo-2020-0010
Publisher site
See Article on Publisher Site

Abstract

AbstractIn 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.

Journal

Dependence Modeling – de Gruyter

Published: Jan 1, 2020

Keywords: Dißmann Algorithm; family-wise error rate; global significance level; Kendall’s τ; local significance levels; multiple testing; 62J15; 62H20; 62E17

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