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A strong law of large numbers related to multiple testing normal means

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  • Chen, Xiongzhi
  • Doerge, R.W.

Abstract

We prove a strong law of large numbers for simultaneously testing whether the means of a set of dependent normal random variables are zero. Our result can be used to check whether the widely-used “weak dependence” assumption holds.

Suggested Citation

  • Chen, Xiongzhi & Doerge, R.W., 2020. "A strong law of large numbers related to multiple testing normal means," Statistics & Probability Letters, Elsevier, vol. 159(C).
    • Handle: RePEc:eee:stapro:v:159:y:2020:i:c:s0167715219303396
    DOI: 10.1016/j.spl.2019.108693
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    References listed on IDEAS

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    1. Art B. Owen, 2005. "Variance of the number of false discoveries," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 411-426, June.
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    4. John D. Storey & Jonathan E. Taylor & David Siegmund, 2004. "Strong control, conservative point estimation and simultaneous conservative consistency of false discovery rates: a unified approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 187-205, February.
    5. David Azriel & Armin Schwartzman, 2015. "The Empirical Distribution of a Large Number of Correlated Normal Variables," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(511), pages 1217-1228, September.
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    Cited by:

    1. Chen, Xiongzhi, 2020. "A strong law of large numbers for simultaneously testing parameters of Lancaster bivariate distributions," Statistics & Probability Letters, Elsevier, vol. 167(C).

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