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Stepwise Multiple Testing as Formalized Data Snooping

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  • Joseph P. Romano
  • 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. 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 modified to other contexts, such as making inference for the individual regression coefficients 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.

Suggested Citation

  • Joseph P. Romano & Michael Wolf, 2003. "Stepwise Multiple Testing as Formalized Data Snooping," Working Papers 17, Barcelona Graduate School of Economics.
  • Handle: RePEc:bge:wpaper:17
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    File URL: http://www.barcelonagse.eu/sites/default/files/working_paper_pdfs/17.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. Lovell, Michael C, 1983. "Data Mining," The Review of Economics and Statistics, MIT Press, vol. 65(1), pages 1-12, February.
    3. 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.
    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. Lo, Andrew W & MacKinlay, A Craig, 1990. "Data-Snooping Biases in Tests of Financial Asset Pricing Models," Review of Financial Studies, Society for Financial Studies, vol. 3(3), pages 431-467.
    6. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    7. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
    8. Leamer, Edward E, 1983. "Let's Take the Con Out of Econometrics," American Economic Review, American Economic Association, vol. 73(1), pages 31-43, March.
    9. Andrews, Donald W K & Monahan, J Christopher, 1992. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Econometrica, Econometric Society, vol. 60(4), pages 953-966, July.
    10. Gonzalo, Jesus & Wolf, Michael, 2005. "Subsampling inference in threshold autoregressive models," Journal of Econometrics, Elsevier, vol. 127(2), pages 201-224, August.
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    More about this item

    Keywords

    Bootstrap; data snooping; familywise error; multiple testing; step-down method;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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