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Bootstrap hypothesis testing in regression models


  • Paparoditis, Efstathios
  • Politis, Dimitris N.


The paper investigates how the particular choice of residuals used in a bootstrap-based testing procedure affects the properties of the test. The properties of the tests are investigated both under the null and under the alternative. It is shown that for non-pivotal test statistics, the method used to obtain residuals largely affects the power behavior of the tests. For instance, imposing the null hypothesis in the residual estimation step--although it does not affect the behavior of the test if the null is true--it leads to a loss of power under the alternative as compared to tests based on resampling unrestricted residuals. Residuals obtained using a parameter estimator which minimizes their variance maximizes the power of the corresponding bootstrap-based tests. In this context, studentizing makes the tests more robust to such residual effects.

Suggested Citation

  • Paparoditis, Efstathios & Politis, Dimitris N., 2005. "Bootstrap hypothesis testing in regression models," Statistics & Probability Letters, Elsevier, vol. 74(4), pages 356-365, October.
  • Handle: RePEc:eee:stapro:v:74:y:2005:i:4:p:356-365

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    References listed on IDEAS

    1. Anders Rygh Swensen, 2003. "Bootstrapping unit root tests for integrated processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 99-126, January.
    2. Joon Y. Park, 2003. "Bootstrap Unit Root Tests," Econometrica, Econometric Society, vol. 71(6), pages 1845-1895, November.
    3. Horowitz, Joel L., 1994. "Bootstrap-based critical values for the information matrix test," Journal of Econometrics, Elsevier, vol. 61(2), pages 395-411, April.
    4. Nankervis, John C & Savin, N E, 1996. "The Level and Power of the Bootstrap t Test in the AR(1) Model with Trend," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(2), pages 161-168, April.
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    Cited by:

    1. Cavaliere, Giuseppe & Nielsen, Morten Ørregaard & Taylor, A.M. Robert, 2015. "Bootstrap score tests for fractional integration in heteroskedastic ARFIMA models, with an application to price dynamics in commodity spot and futures markets," Journal of Econometrics, Elsevier, vol. 187(2), pages 557-579.
    2. Götz, Thomas B. & Hecq, Alain & Smeekes, Stephan, 2016. "Testing for Granger causality in large mixed-frequency VARs," Journal of Econometrics, Elsevier, vol. 193(2), pages 418-432.
    3. Robinson, Peter M. & Rossi, Francesca, 2012. "Improved tests for spatial correlation," MPRA Paper 41835, University Library of Munich, Germany.
    4. James G. MacKinnon, 2012. "Thirty Years of Heteroskedasticity-Robust Inference," Working Papers 1268, Queen's University, Department of Economics.
    5. Berg, Arthur & McMurry, Timothy L. & Politis, Dimitris N., 2010. "Subsampling p-values," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1358-1364, September.
    6. Robinson, Peter M. & Rossi, Francesca, 2015. "Refined Tests For Spatial Correlation," Econometric Theory, Cambridge University Press, vol. 31(06), pages 1249-1280, December.
    7. repec:cep:stiecm:/2013/565 is not listed on IDEAS


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