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The multivariate-t distribution and the Simes inequality

Author

Listed:
  • Block, Henry W.
  • Savits, Thomas H.
  • Wang, Jie
  • Sarkar, Sanat K.

Abstract

Sarkar (1998) showed that certain positively dependent (MTP2) random variables satisfy the Simes inequality. The multivariate-t distribution does not satisfy this (MTP2) property, so other means are necessary. A corollary was given in Sarkar (1998) to handle this distribution, but there is an error. In this paper a direct proof is given to show the multivariate-t does satisfy the Simes inequality.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:1:p:227-232
    DOI: 10.1016/j.spl.2012.08.013
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    References listed on IDEAS

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    1. Sampson, Allan R., 1983. "Positive dependence properties of elliptically symmetric distributions," Journal of Multivariate Analysis, Elsevier, vol. 13(2), pages 375-381, June.
    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).
    2. 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.

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