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

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

Abstract

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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Bibliographic Info

Paper provided by Institute for Empirical Research in Economics - University of Zurich in its series IEW - Working Papers with number 337.

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Date of creation: Dec 2008
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Handle: RePEc:zur:iewwpx:337

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

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References

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  1. 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.
  2. Abramovich, Felix & Benjamini, Yoav, 1996. "Adaptive thresholding of wavelet coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 22(4), pages 351-361, August.
  3. Donald W.K. Andrews & Christopher J. Monahan, 1990. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Cowles Foundation Discussion Papers 942, Cowles Foundation for Research in Economics, Yale University.
  4. 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.
  5. Joseph P. Romano & Michael Wolf, 2006. "Improved Nonparametric Confidence Intervals in Time Series Regressions," IEW - Working Papers 273, Institute for Empirical Research in Economics - University of Zurich.
  6. 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.
  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. Joseph P. Romano & Azeem M. Shaikh & Michael Wolf, 2010. "multiple testing," The New Palgrave Dictionary of Economics, Palgrave Macmillan.
  9. 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.
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Citations

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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. 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.
  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. 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).
  5. Joseph P. Romano & Azeem M. Shaikh & Michael Wolf, 2009. "Hypothesis testing in econometrics," IEW - Working Papers 444, Institute for Empirical Research in Economics - University of Zurich.
  6. 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.
  7. Uwe Hassler & Verena Werkmann, 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), Justus-Liebig University Giessen, Department of Statistics and Economics, vol. 234(1), pages 23-43, January.
  8. Huber, Martin & Mellace, Giovanni, 2011. "Testing instrument validity for LATE identification based on inequality moment constraints," Economics Working Paper Series 1143, University of St. Gallen, School of Economics and Political Science.
  9. Nik Tuzov & Frederi Viens, 2011. "Mutual fund performance: false discoveries, bias, and power," Annals of Finance, Springer, vol. 7(2), pages 137-169, May.
  10. Deckers, Thomas & Hanck, Christoph, 2009. "Multiple Testing Techniques in Growth Econometrics," MPRA Paper 17843, University Library of Munich, Germany.
  11. 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.

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