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Control of the false discovery rate under dependence using the bootstrap and subsampling

  • Joseph Romano

    ()

  • Azeem 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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File URL: http://hdl.handle.net/10.1007/s11749-008-0126-6
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Article provided by Springer in its journal TEST.

Volume (Year): 17 (2008)
Issue (Month): 3 (November)
Pages: 417-442

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Handle: RePEc:spr:testjl:v:17:y:2008:i:3:p:417-442
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  1. 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.
  2. Joseph P & Romano & Azeem M. Shaikh & Michael Wolf, 2005. "Formalized Data Snooping Based on Generalized Error Rates," IEW - Working Papers 259, Institute for Empirical Research in Economics - University of Zurich.
  3. 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.
  4. Joseph P. Romano & Michael Wolf, 2002. "Improved nonparametric confidence intervals in time series regressions," Economics Working Papers 635, Department of Economics and Business, Universitat Pompeu Fabra.
  5. 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.
  6. Joe, Harry, 2006. "Generating random correlation matrices based on partial correlations," Journal of Multivariate Analysis, Elsevier, vol. 97(10), pages 2177-2189, November.
  7. Abramovich, Felix & Benjamini, Yoav, 1996. "Adaptive thresholding of wavelet coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 22(4), pages 351-361, August.
  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. Joseph P. Romano & Azeem M. Shaikh & Michael Wolf, 2010. "multiple testing," The New Palgrave Dictionary of Economics, Palgrave Macmillan.
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