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Where to find needles in a haystack?

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  • Zhigen Zhao

    (Temple University)

Abstract

In many existing methods of multiple comparison, one starts with either Fisher’s p value or the local fdr. One commonly used p value, defined as the tail probability exceeding the observed test statistic under the null distribution, fails to use information from the distribution under the alternative hypothesis. The targeted region of signals could be wrong when the likelihood ratio is not monotone. The oracle local fdr based approaches could be optimal because they use the probability density functions of the test statistic under both the null and alternative hypotheses. However, the data-driven version could be problematic because of the difficulty and challenge of probability density function estimation. In this paper, we propose a new method, Cdf and Local fdr Assisted multiple Testing method (CLAT), which is optimal for cases when the p value based methods are optimal and for some other cases when p value based methods are not. Additionally, CLAT only relies on the empirical distribution function which quickly converges to the oracle one. Both the simulations and real data analysis demonstrate the superior performance of the CLAT method. Furthermore, the computation is instantaneous based on a novel algorithm and is scalable to large data sets.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:31:y:2022:i:1:d:10.1007_s11749-021-00775-x
    DOI: 10.1007/s11749-021-00775-x
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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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    6. Hongyuan Cao & Wenguang Sun & Michael R. Kosorok, 2013. "The optimal power puzzle: scrutiny of the monotone likelihood ratio assumption in multiple testing," Biometrika, Biometrika Trust, vol. 100(2), pages 495-502.
    7. 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.
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