  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 Sidak-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.
