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Bootstrap hypothesis testing in regression models

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  • Paparoditis, Efstathios
  • Politis, Dimitris N.
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    Abstract

    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 74 (2005)
    Issue (Month): 4 (October)
    Pages: 356-365

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    Handle: RePEc:eee:stapro:v:74:y:2005:i:4:p:356-365

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    Keywords: Hypothesis testing Parametric models Resampling Residuals;

    References

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    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, 01.
    2. Joon Y. Park, 2000. "Bootstrap Unit Root Tests," Econometric Society World Congress 2000 Contributed Papers 1587, Econometric Society.
    3. 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 161-68, April.
    4. Horowitz, Joel L., 1994. "Bootstrap-based critical values for the information matrix test," Journal of Econometrics, Elsevier, vol. 61(2), pages 395-411, April.
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    Cited by:
    1. James G. MacKinnon, 2012. "Thirty Years of Heteroskedasticity-Robust Inference," Working Papers 1268, Queen's University, Department of Economics.
    2. Giuseppe Cavaliere & Morten Ørregaard Nielsen & A.M. Robert Taylor, 2014. "Bootstrap Score Tests for Fractional Integration in Heteroskedastic ARFIMA Models, with an Application to Price Dynamics in Commodity Spot and Futures Markets," CREATES Research Papers 2014-22, School of Economics and Management, University of Aarhus.
    3. Robinson, Peter M. & Rossi, Francesca, 2012. "Improved tests for spatial correlation," MPRA Paper 41835, University Library of Munich, Germany.

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