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Formalized Data Snooping Based on Generalized Error Rates

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

Abstract

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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Bibliographic Info

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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Keywords: Data snooping; false discovery proportion; false discovery rate; generalized familywise error rate; model selection; multiple testing; stepwise methods;

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  1. 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.
  2. Allan Timmermann & Halbert White & Ryan Sullivan, 1998. "Data-Snooping, Technical Trading, Rule Performance and the Bootstrap," FMG Discussion Papers dp303, Financial Markets Group.
  3. Hansen, Peter Reinhard, 2005. "A Test for Superior Predictive Ability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 365-380, October.
  4. Joseph P. Romano & Michael Wolf, 2001. "Improved Nonparametric Confidence Intervals In Time Series Regressions," Statistics and Econometrics Working Papers ws010201, Universidad Carlos III, Departamento de Estadística y Econometría.
  5. 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.
  6. Joseph P. Romano & Michael Wolf, 2005. "Exact and Approximate Stepdown Methods for Multiple Hypothesis Testing," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 94-108, March.
  7. Abramovich, Felix & Benjamini, Yoav, 1996. "Adaptive thresholding of wavelet coefficients," Computational Statistics & Data Analysis, Elsevier, vol. 22(4), pages 351-361, August.
  8. Hans-Martin Krolzig & David Hendry, 1999. "Computer Automation of General-to-Specific Model Selection Procedures," Computing in Economics and Finance 1999 314, Society for Computational Economics.
  9. Timmermann, Allan G, 2005. "Forecast Combinations," CEPR Discussion Papers 5361, C.E.P.R. Discussion Papers.
  10. Joseph P. Romano & Michael Wolf, 2005. "Stepwise Multiple Testing as Formalized Data Snooping," Econometrica, Econometric Society, vol. 73(4), pages 1237-1282, 07.
  11. Joseph P. Romano & Azeem M. Shaikh & Michael Wolf, 2010. "multiple testing," The New Palgrave Dictionary of Economics, Palgrave Macmillan.
  12. 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.
  13. Hidetoshi Shimodaira, 1998. "An Application of Multiple Comparison Techniques to Model Selection," Annals of the Institute of Statistical Mathematics, Springer, vol. 50(1), pages 1-13, March.
  14. Peter Reinhard Hansen & Asger Lunde & James M. Nason, 2005. "Model confidence sets for forecasting models," Working Paper 2005-07, Federal Reserve Bank of Atlanta.
  15. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-66, July.
  16. 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.
  17. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
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