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The Power of Bootstrap and Asymptotic Tests

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  • Russell Davidson

    ()
    (McGill University)

  • James G. MacKinnon

    ()
    (Queen's University)

Abstract

We introduce the concept of the bootstrap discrepancy, which measures the difference in rejection probabilities between a bootstrap test based on a given test statistic and that of a (usually infeasible) test based on the true distribution of the statistic. We show that the bootstrap discrepancy is of the same order of magnitude under the null hypothesis and under non-null processes described by a Pitman drift. However, complications arise in the measurement of power. If the test statistic is not an exact pivot, critical values depend on which data-generating process (DGP) is used to determine the distribution under the null hypothesis. We propose as the proper choice the DGP which minimizes the bootstrap discrepancy. We also show that, under an asymptotic independence condition, the power of both bootstrap and asymptotic tests can be estimated cheaply by simulation. The theory of the paper and the proposed simulation method are illustrated by Monte Carlo experiments using the logit model.

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File URL: http://qed.econ.queensu.ca/working_papers/papers/qed_wp_1035.pdf
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Bibliographic Info

Paper provided by Queen's University, Department of Economics in its series Working Papers with number 1035.

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Length: 22 pages
Date of creation: Jul 2004
Date of revision:
Publication status: Forthcoming in Journal of Econometrics
Handle: RePEc:qed:wpaper:1035

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Keywords: bootstrap test; bootstrap discrepancy; Pitman drift; drifting DGP; Monte Carlo; test power; power; asymptotic test;

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References

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  1. Russell Davidson & James G. MacKinnon, 1994. "Graphical Methods for Investigating the Size and Power of Hypothesis Tests," Working Papers 903, Queen's University, Department of Economics.
  2. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
  3. Russell Davidson & James G. MacKinnon, 1982. "Convenient Specification Tests for Logit and Probit Models," Working Papers 514, Queen's University, Department of Economics.
  4. Davidson, Russell & MacKinnon, James G, 1987. "Implicit Alternatives and the Local Power of Test Statistics," Econometrica, Econometric Society, vol. 55(6), pages 1305-29, November.
  5. Horowitz, Joel L. & Savin, N. E., 2000. "Empirically relevant critical values for hypothesis tests: A bootstrap approach," Journal of Econometrics, Elsevier, vol. 95(2), pages 375-389, April.
  6. Davidson, Russell & MacKinnon, James G., 1999. "The Size Distortion Of Bootstrap Tests," Econometric Theory, Cambridge University Press, vol. 15(03), pages 361-376, June.
  7. Russell Davidson & James MacKinnon, 2000. "Bootstrap tests: how many bootstraps?," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 55-68.
  8. Rudolf Beran, 1997. "Diagnosing Bootstrap Success," Annals of the Institute of Statistical Mathematics, Springer, vol. 49(1), pages 1-24, March.
  9. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, October.
  10. 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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