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The effect of correlation in false discovery rate estimation

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  • Armin Schwartzman
  • Xihong Lin

Abstract

The objective of this paper is to quantify the effect of correlation in false discovery rate analysis. Specifically, we derive approximations for the mean, variance, distribution and quantiles of the standard false discovery rate estimator for arbitrarily correlated data. This is achieved using a negative binomial model for the number of false discoveries, where the parameters are found empirically from the data. We show that correlation may increase the bias and variance of the estimator substantially with respect to the independent case, and that in some cases, such as an exchangeable correlation structure, the estimator fails to be consistent as the number of tests becomes large. Copyright 2011, Oxford University Press.

Suggested Citation

  • Armin Schwartzman & Xihong Lin, 2011. "The effect of correlation in false discovery rate estimation," Biometrika, Biometrika Trust, vol. 98(1), pages 199-214.
    • Handle: RePEc:oup:biomet:v:98:y:2011:i:1:p:199-214
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    File URL: http://hdl.handle.net/10.1093/biomet/asq075
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    Cited by:

    1. Jianqing Fan & Xu Han, 2017. "Estimation of the false discovery proportion with unknown dependence," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 1143-1164, September.
    2. Ian Barnett & Rajarshi Mukherjee & Xihong Lin, 2017. "The Generalized Higher Criticism for Testing SNP-Set Effects in Genetic Association Studies," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 64-76, January.
    3. Ghosh Debashis, 2012. "Incorporating the Empirical Null Hypothesis into the Benjamini-Hochberg Procedure," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(4), pages 1-21, July.
    4. Sairam Rayaprolu & Zhiyi Chi, 2021. "False Discovery Variance Reduction in Large Scale Simultaneous Hypothesis Tests," Methodology and Computing in Applied Probability, Springer, vol. 23(3), pages 711-733, September.
    5. Sean M Devlin & Axel Martin & Irina Ostrovnaya, 2021. "Identifying prognostic pairwise relationships among bacterial species in microbiome studies," PLOS Computational Biology, Public Library of Science, vol. 17(11), pages 1-12, November.
    6. Arnab Maity & Xihong Lin, 2011. "Powerful Tests for Detecting a Gene Effect in the Presence of Possible Gene–Gene Interactions Using Garrote Kernel Machines," Biometrics, The International Biometric Society, vol. 67(4), pages 1271-1284, December.
    7. Wang, Jiangzhou & Cui, Tingting & Zhu, Wensheng & Wang, Pengfei, 2023. "Covariate-modulated large-scale multiple testing under dependence," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    8. 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).
    9. Can Shao & Jun Li & Ying Cheng, 2016. "Detection of Test Speededness Using Change-Point Analysis," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 1118-1141, December.
    10. 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.
    11. Noirrit Kiran Chandra & Sourabh Bhattacharya, 2021. "Asymptotic theory of dependent Bayesian multiple testing procedures under possible model misspecification," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(5), pages 891-920, October.
    12. Benjamin R. Auer, 2022. "On false discoveries of standard t-tests in investment management applications," Review of Managerial Science, Springer, vol. 16(3), pages 751-768, April.
    13. 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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