WIAS Preprint No. 1967, (2014)

On the Simes inequality in elliptical models



Authors

  • Bodnar, Taras
  • Dickhaus, Thorsten

2010 Mathematics Subject Classification

  • 60E15 62J15 62F03

Keywords

  • Covariance matrix, distributional transform, multiple testing, multivariate normal distribution, p-value, Student's t, total positivity

Abstract

We provide necessary and sufficient conditions for the validity of the inequality of Simes (1986) in models with elliptical dependencies. Necessary conditions are presented in terms of sufficient conditions for the reverse Simes inequality. One application of our main results concerns the problem of model misspecification, in particular the case that the assumption of Gaussianity of test statistics is violated. Since our sufficient conditions require non-negativity of correlation coefficients between test statistics, we also develop exact tests for vectors of correlation coefficients.

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