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Capturing the severity of type II errors in high-dimensional multiple testing

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  • He, Li
  • Sarkar, Sanat K.
  • Zhao, Zhigen

Abstract

The severity of type II errors is frequently ignored when deriving a multiple testing procedure, even though utilizing it properly can greatly help in making correct decisions. This paper puts forward a theory behind developing a multiple testing procedure that can incorporate the type II error severity and is optimal in the sense of minimizing a measure of false non-discoveries among all procedures controlling a measure of false discoveries. The theory is developed under a general model allowing arbitrary dependence by taking a compound decision theoretic approach to multiple testing with a loss function incorporating the type II error severity. We present this optimal procedure in its oracle form and offer numerical evidence of its superior performance over relevant competitors.

Suggested Citation

  • He, Li & Sarkar, Sanat K. & Zhao, Zhigen, 2015. "Capturing the severity of type II errors in high-dimensional multiple testing," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 106-116.
    • Handle: RePEc:eee:jmvana:v:142:y:2015:i:c:p:106-116
    DOI: 10.1016/j.jmva.2015.08.005
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    References listed on IDEAS

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    1. Sun, Wenguang & Cai, T. Tony, 2007. "Oracle and Adaptive Compound Decision Rules for False Discovery Rate Control," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 901-912, September.
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    Cited by:

    1. Pengfei Wang & Wensheng Zhu, 2022. "Large‐scale covariate‐assisted two‐sample inference under dependence," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1421-1447, December.
    2. Zhigen Zhao, 2022. "Where to find needles in a haystack?," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(1), pages 148-174, March.
    3. Wang, Xia & Shojaie, Ali & Zou, Jian, 2019. "Bayesian hidden Markov models for dependent large-scale multiple testing," Computational Statistics & Data Analysis, Elsevier, vol. 136(C), pages 123-136.

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