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Some Results on the Control of the False Discovery Rate under Dependence

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  • ALESSIO FARCOMENI

Abstract

. Controlling the false discovery rate (FDR) is a powerful approach to multiple testing, with procedures developed with applications in many areas. Dependence among the test statistics is a common problem, and many attempts have been made to extend the procedures. In this paper, we show that a certain degree of dependence is allowed among the test statistics, when the number of tests is large, with no need for any correction. We then suggest a way to conservatively estimate the proportion of false nulls, both under dependence and independence, and discuss the advantages of using such estimators when controlling the FDR.

Suggested Citation

  • Alessio Farcomeni, 2007. "Some Results on the Control of the False Discovery Rate under Dependence," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(2), pages 275-297, June.
    • Handle: RePEc:bla:scjsta:v:34:y:2007:i:2:p:275-297
    DOI: 10.1111/j.1467-9469.2006.00530.x
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    References listed on IDEAS

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    1. John Storey & Jeffrey Leek & Wenzhong Xiao & James Dai & Ron Davis, 2004. "A Significance Method for Time Course Microarray Experiments Applied to Two Human Studies," UW Biostatistics Working Paper Series 1065, Berkeley Electronic Press.
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    Cited by:

    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.
    2. Alessio Farcomeni & Antonio Punzo, 2020. "Robust model-based clustering with mild and gross outliers," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(4), pages 989-1007, December.
    3. Hai Shu & Bin Nan & Robert Koeppe, 2015. "Multiple testing for neuroimaging via hidden Markov random field," Biometrics, The International Biometric Society, vol. 71(3), pages 741-750, September.
    4. Gontscharuk, Veronika & Finner, Helmut, 2013. "Asymptotic FDR control under weak dependence: A counterexample," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1888-1893.
    5. Cerioli, Andrea & Farcomeni, Alessio, 2011. "Error rates for multivariate outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 544-553, January.
    6. L. Finos & A. Farcomeni, 2011. "k-FWER Control without p -value Adjustment, with Application to Detection of Genetic Determinants of Multiple Sclerosis in Italian Twins," Biometrics, The International Biometric Society, vol. 67(1), pages 174-181, March.
    7. Lee, Donghwan & Lee, Youngjo, 2016. "Extended likelihood approach to multiple testing with directional error control under a hidden Markov random field model," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 1-13.
    8. A. Farcomeni & L. Finos, 2013. "FDR Control with Pseudo-Gatekeeping Based on a Possibly Data Driven Order of the Hypotheses," Biometrics, The International Biometric Society, vol. 69(3), pages 606-613, September.
    9. Alessio Farcomeni, 2009. "Generalized Augmentation to Control the False Discovery Exceedance in Multiple Testing," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(3), pages 501-517, September.
    10. T. Tony Cai & Weidong Liu, 2016. "Large-Scale Multiple Testing of Correlations," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(513), pages 229-240, March.
    11. Delattre, S. & Roquain, E., 2011. "On the false discovery proportion convergence under Gaussian equi-correlation," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 111-115, January.
    12. Andrew Y. Chen & Tom Zimmermann, 2022. "Publication Bias in Asset Pricing Research," Papers 2209.13623, arXiv.org, revised Sep 2023.
    13. Axel Gandy & Georg Hahn, 2014. "MMCTest—A Safe Algorithm for Implementing Multiple Monte Carlo Tests," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 1083-1101, December.
    14. Dean Palejev & Mladen Savov, 2021. "On the Convergence of the Benjamini–Hochberg Procedure," Mathematics, MDPI, vol. 9(17), pages 1-19, September.
    15. 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.
    16. Farcomeni Alessio & Arima Serena, 2012. "A Bayesian autoregressive three-state hidden Markov model for identifying switching monotonic regimes in Microarray time course data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(4), pages 1-31, June.
    17. 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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