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Formalized Data Snooping Based on Generalized Error Rates

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

It is common in econometric applications that several hypothesis tests are carried out at the same time. The problem then becomes how to decide which hypotheses to reject, accounting for the multitude of tests. The classical approach is to control the familywise error rate (FWE), that is, the probability of one or more false rejections. But when the number of hypotheses under consideration is large, control of the FWE can become too demanding. As a result, the number of false hypotheses rejected may be small or even zero. This suggests replacing control of the FWE by a more liberal measure. To this end, we review a number of proposals from the statistical literature. We briefly discuss how these procedures apply to the general problem of model selection. A simulation study and two empirical applications illustrate the methods.

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Paper provided by Institute for Empirical Research in Economics - University of Zurich in its series IEW - Working Papers with number 259.

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Date of creation: Dec 2005
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Handle: RePEc:zur:iewwpx:259
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  1. David Hendry & Hans-Martin Krolzig, 2000. "Computer Automation of General-to-Specific Model Selection Procedures," Economics Series Working Papers 3, University of Oxford, Department of Economics.
  2. Joseph P. Romano & Michael Wolf, 2003. "Stepwise multiple testing as formalized data snooping," Economics Working Papers 712, Department of Economics and Business, Universitat Pompeu Fabra.
  3. Peter Hansen & Asger Lunde & James M. Nason, 2003. "Choosing the Best Volatility Models:The Model Confidence Set Approach," Working Papers 2003-05, Brown University, Department of Economics.
  4. Marco Aiolfi & Carlos Capistrán & Allan Timmermann, 2010. "Forecast Combinations," Working Papers 2010-04, Banco de México.
  5. 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.
  6. Kabaila, Paul & Leeb, Hannes, 2006. "On the Large-Sample Minimal Coverage Probability of Confidence Intervals After Model Selection," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 619-629, June.
  7. Hidetoshi Shimodaira, 1998. "An Application of Multiple Comparison Techniques to Model Selection," Annals of the Institute of Statistical Mathematics, The Institute of Statistical Mathematics, vol. 50(1), pages 1-13, March.
  8. Wolf, Michael & Romano, Joseph P., 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.
  9. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
  10. Ryan Sullivan & Allan Timmermann & Halbert White, 1999. "Data-Snooping, Technical Trading Rule Performance, and the Bootstrap," Journal of Finance, American Finance Association, vol. 54(5), pages 1647-1691, October.
  11. Abramovich, Felix & Benjamini, Yoav, 1996. "Adaptive thresholding of wavelet coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 22(4), pages 351-361, August.
  12. Sullivan, Ryan & Timmermann, Allan & White, Halbert, 2001. "Dangers of data mining: The case of calendar effects in stock returns," Journal of Econometrics, Elsevier, vol. 105(1), pages 249-286, November.
  13. Hansen, Peter Reinhard, 2005. "A Test for Superior Predictive Ability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 365-380, October.
  14. Peter Reinhard Hansen & Asger Lunde & James M. Nason, 2005. "Model confidence sets for forecasting models," FRB Atlanta Working Paper 2005-07, Federal Reserve Bank of Atlanta.
  15. Joseph P. Romano & Azeem M. Shaikh & Michael Wolf, 2010. "multiple testing," The New Palgrave Dictionary of Economics, Palgrave Macmillan.
  16. Xiaotong Shen & Hsin-Cheng Huang & Jimmy Ye, 2004. "Inference After Model Selection," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 751-762, January.
  17. Joseph Romano & Michael Wolf, 2003. "Exact and approximate stepdown methods for multiple hypothesis testing," Economics Working Papers 727, Department of Economics and Business, Universitat Pompeu Fabra.
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