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Control of the False Discovery Rate under Dependence using the Bootstrap and Subsampling


  • Joseph P. Romano
  • Azeem M. Shaikh
  • Michael Wolf


This paper considers the problem of testing s null hypotheses simultaneously while controlling the false discovery rate (FDR). Benjamini and Hochberg (1995) provide a method for controlling the FDR based on p-values for each of the null hypotheses under the assumption that the p-values are independent. Subsequent research has since shown that this procedure is valid under weaker assumptions on the joint distribution of the p-values. Related procedures that are valid under no assumptions on the joint distribution of the p-values have also been developed. None of these procedures, however, incorporate information about the dependence structure of the test statistics. This paper develops methods for control of the FDR under weak assumptions that incorporate such information and, by doing so, are better able to detect false null hypotheses. We illustrate this property via a simulation study and two empirical applications. In particular, the bootstrap method is competitive with methods that require independence if independence holds, but it outperforms these methods under dependence.

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  • Joseph P. Romano & Azeem M. Shaikh & Michael Wolf, 2008. "Control of the False Discovery Rate under Dependence using the Bootstrap and Subsampling," IEW - Working Papers 337, Institute for Empirical Research in Economics - University of Zurich.
  • Handle: RePEc:zur:iewwpx:337

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    References listed on IDEAS

    1. Yoav Benjamini & Abba M. Krieger & Daniel Yekutieli, 2006. "Adaptive linear step-up procedures that control the false discovery rate," Biometrika, Biometrika Trust, vol. 93(3), pages 491-507, September.
    2. Romano, Joseph P. & Wolf, Michael, 2001. "Improved nonparametric confidence intervals in time series regressions," DES - Working Papers. Statistics and Econometrics. WS ws010201, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Romano, Joseph P. & Shaikh, Azeem M. & Wolf, Michael, 2008. "Formalized Data Snooping Based On Generalized Error Rates," Econometric Theory, Cambridge University Press, vol. 24(02), pages 404-447, April.
    4. van der Laan Mark J. & Dudoit Sandrine & Pollard Katherine S., 2004. "Augmentation Procedures for Control of the Generalized Family-Wise Error Rate and Tail Probabilities for the Proportion of False Positives," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 3(1), pages 1-27, June.
    5. Abramovich, Felix & Benjamini, Yoav, 1996. "Adaptive thresholding of wavelet coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 22(4), pages 351-361, August.
    6. Joseph P. Romano & Azeem M. Shaikh & Michael Wolf, 2010. "multiple testing," The New Palgrave Dictionary of Economics, Palgrave Macmillan.
    7. Joe, Harry, 2006. "Generating random correlation matrices based on partial correlations," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2177-2189, November.
    8. 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.
    9. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
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    Cited by:

    1. Miecznikowski, Jeffrey C. & Gold, David & Shepherd, Lori & Liu, Song, 2011. "Deriving and comparing the distribution for the number of false positives in single step methods to control k-FWER," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1695-1705, November.
    2. 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.
    3. Joseph P. Romano & Michael Wolf, 2008. "Balanced Control of Generalized Error Rates," IEW - Working Papers 379, Institute for Empirical Research in Economics - University of Zurich.
    4. Galizzi, Matteo M. & Navarro-Martínez, Daniel, 2018. "On the external validity of social preference games: a systematic lab-field study," LSE Research Online Documents on Economics 84088, London School of Economics and Political Science, LSE Library.
    5. Smeekes Stephan, 2011. "Bootstrap Sequential Tests to Determine the Stationary Units in a Panel," Research Memorandum 003, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    6. Deckers, Thomas & Hanck, Christoph, 2009. "Multiple Testing Techniques in Growth Econometrics," MPRA Paper 17843, University Library of Munich, Germany.
    7. de Uña-Alvarez Jacobo, 2012. "The Beta-Binomial SGoF method for multiple dependent tests," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 11(3), pages 1-32, May.
    8. Moon, H.R. & Perron, B., 2012. "Beyond panel unit root tests: Using multiple testing to determine the nonstationarity properties of individual series in a panel," Journal of Econometrics, Elsevier, vol. 169(1), pages 29-33.
    9. Ferreira José A. & Berkhof Johannes & Souverein Olga & Zwinderman Koos, 2009. "A Multiple Testing Approach to High-Dimensional Association Studies with an Application to the Detection of Associations between Risk Factors of Heart Disease and Genetic Polymorphisms," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 8(1), pages 1-56, January.
    10. Hassler Uwe & Werkmann Verena, 2014. "Multiple Comparisons and Joint Significance in Panel Unit Root Testing with Evidence on International Interest Rate Linkage," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 234(1), pages 23-43, February.
    11. Roland G. Fryer, Jr. & Steven D. Levitt & John A. List, 2015. "Parental Incentives and Early Childhood Achievement: A Field Experiment in Chicago Heights," NBER Working Papers 21477, National Bureau of Economic Research, Inc.
    12. Martin Huber & Giovanni Mellace, 2015. "Testing Instrument Validity for LATE Identification Based on Inequality Moment Constraints," The Review of Economics and Statistics, MIT Press, vol. 97(2), pages 398-411, May.
    13. Joseph P. Romano & Azeem M. Shaikh & Michael Wolf, 2010. "Hypothesis Testing in Econometrics," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 75-104, September.
    14. Westerlund, Joakim & Thuraisamy, Kannan & Sharma, Susan, 2015. "On the use of panel cointegration tests in energy economics," Energy Economics, Elsevier, vol. 50(C), pages 359-363.
    15. repec:sbe:breart:v:31:y:2011:i:2:a:7173 is not listed on IDEAS
    16. Giuseppe Cavaliere & Dimitris N. Politis & Anders Rahbek & Stephan Smeekes, 2015. "Recent developments in bootstrap methods for dependent data," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(3), pages 398-415, May.
    17. Li Wang & Xingzhong Xu & Yong A, 2016. "New multiple testing method under no dependency assumption, with application to multiple comparisons problem," Statistical Papers, Springer, vol. 57(1), pages 161-183, March.
    18. Márcio Laurini, 2012. "Generalized Tests of Investment Fund Performance," IBMEC RJ Economics Discussion Papers 2012-03, Economics Research Group, IBMEC Business School - Rio de Janeiro.

    More about this item


    Bootstrap; Subsampling; False Discovery Rate; Multiple Testing; Stepdown Procedure.;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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