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On the Simes inequality in elliptical models

Author

Listed:
  • Taras Bodnar

    (Stockholm University)

  • Thorsten Dickhaus

    (University of Bremen)

Abstract

We provide some necessary and some sufficient conditions for the validity of the inequality of Simes 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 two exact tests for vectors of correlation coefficients and compare their powers in computer simulations.

Suggested Citation

  • Taras Bodnar & Thorsten Dickhaus, 2017. "On the Simes inequality in elliptical models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 69(1), pages 215-230, February.
    • Handle: RePEc:spr:aistmt:v:69:y:2017:i:1:d:10.1007_s10463-015-0539-4
    DOI: 10.1007/s10463-015-0539-4
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    References listed on IDEAS

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    1. Block, Henry W. & Savits, Thomas H. & Wang, Jie & Sarkar, Sanat K., 2013. "The multivariate-t distribution and the Simes inequality," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 227-232.
    2. Block, Henry W. & Savits, Thomas H. & Shaked, Moshe, 1985. "A concept of negative dependence using stochastic ordering," Statistics & Probability Letters, Elsevier, vol. 3(2), pages 81-86, April.
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    Cited by:

    1. Xiong, Peihan & Hu, Taizhong, 2022. "On Samuel’s p-value model and the Simes test under dependence," Statistics & Probability Letters, Elsevier, vol. 187(C).

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