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Stepwise multiple testing as formalized data snooping

  • Joseph P. Romano
  • 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. In this paper, we suggest a stepwise multiple testing procedure which asymptotically controls the familywise error rate at a desired level. Compared to related single-step methods, our procedure is more powerful in the sense that it often will reject more false hypotheses. In addition, we advocate the use of studentization when it is feasible. Unlike some stepwise methods, our method implicitly captures the joint dependence structure of the test statistics, which results in increased ability to detect alternative hypotheses. We prove our method asymptotically controls the familywise error rate under minimal assumptions. We present our methodology in the context of comparing several strategies to a common benchmark and deciding which strategies actually beat the benchmark. However, our ideas can easily be extended and/or modi ed to other contexts, such as making inference for the individual regression coecients in a multiple regression framework. Some simulation studies show the improvements of our methods over previous proposals. We also provide an application to a set of real data.

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Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 712.

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Date of creation: Oct 2003
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Handle: RePEc:upf:upfgen:712
Contact details of provider: Web page: http://www.econ.upf.edu/

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  1. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  2. Gonzalo, Jesus & Wolf, Michael, 2005. "Subsampling inference in threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 127(2), pages 201-224, August.
  3. Edward E. Leamer, 1982. "Let's Take the Con Out of Econometrics," UCLA Economics Working Papers 239, UCLA Department of Economics.
  4. Delgado, Miguel A. & Rodriguez-Poo, Juan M. & Wolf, Michael, 2001. "Subsampling inference in cube root asymptotics with an application to Manski's maximum score estimator," Economics Letters, Elsevier, vol. 73(2), pages 241-250, November.
  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. Andrew W. Lo & A. Craig MacKinlay, 1989. "Data-Snooping Biases in Tests of Financial Asset Pricing Models," NBER Working Papers 3001, National Bureau of Economic Research, Inc.
  7. Lovell, Michael C, 1983. "Data Mining," The Review of Economics and Statistics, MIT Press, vol. 65(1), pages 1-12, February.
  8. 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.
  9. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
  10. Tae-Hwy Lee & Yong Bao & Burak Saltoglu, 2006. "Evaluating predictive performance of value-at-risk models in emerging markets: a reality check," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(2), pages 101-128.
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