WIAS Preprint No. 1862, (2013)

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



Authors

  • Stange, Jens
  • Bodnar, Taras
  • Dickhaus, Thorsten

2010 Mathematics Subject Classification

  • 62J15 62F05 62F03

Keywords

  • Delta method, Gumbel-Hougaard copula, multiple testing, simultaneous test procedure, subset pivotality

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 favour 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.

Appeared in

  • AStA Advances in Statistical Analysis,,issue ( ) pp. --

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