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On False Discovery and Non-discovery Proportions of the Dynamic Adaptive Procedure

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  • Kong Xin-Bing
  • Xu Qin-Feng

Abstract

type="main" xml:id="sjos12121-abs-0001"> This paper studies the asymptotic behaviour of the false discovery and non-discovery proportions of the dynamic adaptive procedure under some dependence structure. A Bahadur-type representation of the cut point in simultaneously performing a large scale of tests is presented. The asymptotic bias decompositions of the false discovery and non-discovery proportions are given under some dependence structure. In addition to existing literatures, we find that the randomness due to the dynamic selection of the tuning parameter in estimating the true null rate serves as a source of the approximation error in the Bahadur representation and enters into the asymptotic bias term of the false discovery proportion and those of the false non-discovery proportion. The theory explains to some extent why some seemingly attractive dynamic adaptive procedures do not outperform the competing fixed adaptive procedures substantially in some situations. Simulations justify our theory and findings.

Suggested Citation

  • Kong Xin-Bing & Xu Qin-Feng, 2015. "On False Discovery and Non-discovery Proportions of the Dynamic Adaptive Procedure," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 530-544, June.
    • Handle: RePEc:bla:scjsta:v:42:y:2015:i:2:p:530-544
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    File URL: http://hdl.handle.net/10.1111/sjos.12121
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    References listed on IDEAS

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    1. Bajgrowicz, Pierre & Scaillet, Olivier, 2012. "Technical trading revisited: False discoveries, persistence tests, and transaction costs," Journal of Financial Economics, Elsevier, vol. 106(3), pages 473-491.
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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. Wenguang Sun & T. Tony Cai, 2009. "Large‐scale multiple testing under dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 393-424, April.
    6. John D. Storey, 2002. "A direct approach to false discovery rates," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 479-498, August.
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