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Stepwise Multiple Testing as Formalized Data Snooping

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  • Joseph P. Romano
  • Michael Wolf

Abstract

In econometric applications, often several hypothesis tests are carried out at once. The problem then becomes how to decide which hypotheses to reject, accounting for the multitude of tests. This paper suggests a stepwise multiple testing procedure that asymptotically controls the familywise error rate. Compared to related single-step methods, the procedure is more powerful and often will reject more false hypotheses. In addition, we advocate the use of studentization when feasible. Unlike some stepwise methods, the method implicitly captures the joint dependence structure of the test statistics, which results in increased ability to detect false hypotheses. The methodology is presented in the context of comparing several strategies to a common benchmark. However, our ideas can easily be extended to other contexts where multiple tests occur. Some simulation studies show the improvements of our methods over previous proposals. We also provide an application to a set of real data. Copyright The Econometric Society 2005.

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Bibliographic Info

Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 73 (2005)
Issue (Month): 4 (07)
Pages: 1237-1282

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Handle: RePEc:ecm:emetrp:v:73:y:2005:i:4:p:1237-1282

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  1. 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.
  2. Edward E. Leamer, 1982. "Let's Take the Con Out of Econometrics," UCLA Economics Working Papers 239, UCLA Department of Economics.
  3. 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.
  4. Gonzalo, Jesus & Wolf, Michael, 2005. "Subsampling inference in threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 127(2), pages 201-224, August.
  5. 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.
  6. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  7. 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.
  8. Lovell, Michael C, 1983. "Data Mining," The Review of Economics and Statistics, MIT Press, vol. 65(1), pages 1-12, February.
  9. 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.
  10. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
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