The power of bootstrap and asymptotic tests
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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- Russell Davidson & James MacKinnon, 2000.
"Bootstrap tests: how many bootstraps?,"
Taylor & Francis Journals, vol. 19(1), pages 55-68.
- Russell Davidson & James G. MacKinnon, 1984.
"Implicit Alternatives and the Local Power of Test Statistics,"
556, Queen's University, Department of Economics.
- 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.
- Davidson , R. & Mackinnon, J.G., 1985. "Implicit alternatives and the local power of test statistics," CORE Discussion Papers 1985025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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.
- Russell Davidson & James G. MacKinnon, 1982.
"Convenient Specification Tests for Logit and Probit Models,"
514, Queen's University, Department of Economics.
- Davidson, Russell & MacKinnon, James G., 1984. "Convenient specification tests for logit and probit models," Journal of Econometrics, Elsevier, vol. 25(3), pages 241-262, July.
- Davidson, Russell & MacKinnon, James G., 1999.
"The Size Distortion Of Bootstrap Tests,"
Cambridge University Press, vol. 15(03), pages 361-376, June.
- White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
- Davidson, Russell & MacKinnon, James G, 1998.
"Graphical Methods for Investigating the Size and Power of Hypothesis Tests,"
The Manchester School of Economic & Social Studies,
University of Manchester, vol. 66(1), pages 1-26, January.
- 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.
- Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, December.
- Rudolf Beran, 1997. "Diagnosing Bootstrap Success," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 49(1), pages 1-24, March.
- 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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