The Size and Power of Bootstrap Tests
Bootstrap tests are tests for which the significance level is calculated by some sort of bootstrap procedure, which may be parametric or nonparametric. We show that, in many circumstances, the size distortion of a bootstrap P value for a test will be one whole order of magnitude smaller than that of the corresponding asymptotic P value. We also show that, at least in the parametric case, the magnitude of the distortion will depend on the shape of what we call the P value function. As regards the power of bootstrap tests, we show that the size-corrected power of a bootstrap test differs from that of the corresponding asymptotic test only by an amount of the same order of magnitude as the size distortion, and of arbitrary sign. Monte Carlo results are presented for two cases of interest: tests for serial correlation and nonnested hypothesis tests. These results confirm and illustrate the utility of our theoretical results, and they also suggest that bootstrap tests will often work extremely well in practice.
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- 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).
- 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.
- Russell Davidson & James G. MacKinnon, 1984. "Implicit Alternatives and the Local Power of Test Statistics," Working Papers 556, Queen's University, Department of Economics.
- Davidson, Russell & MacKinnon, James G., 1992. "Regression-based methods for using control variates in Monte Carlo experiments," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 203-222.
- Weber, N. C., 1984. "On resampling techniques for regression models," Statistics & Probability Letters, Elsevier, vol. 2(5), pages 275-278, October.
- Russell Davidson & James G. MacKinnon, 1980.
"Several Tests for Model Specification in the Presence of Alternative Hypotheses,"
378, Queen's University, Department of Economics.
- Davidson, Russell & MacKinnon, James G, 1981. "Several Tests for Model Specification in the Presence of Alternative Hypotheses," Econometrica, Econometric Society, vol. 49(3), pages 781-93, May.
- Horowitz, Joel L., 1994. "Bootstrap-based critical values for the information matrix test," Journal of Econometrics, Elsevier, vol. 61(2), pages 395-411, April.
- Rothernberg, Thomas J, 1984. "Hypothesis Testing in Linear Models When the Error Covariance Matrix Is Nonscalar," Econometrica, Econometric Society, vol. 52(4), pages 827-42, July.
- Joel L. Horowitz, 1996. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Econometrics 9602009, EconWPA, revised 05 Mar 1996.
- Durbin, J, 1970. "Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors are Lagged Dependent Variables," Econometrica, Econometric Society, vol. 38(3), pages 410-21, May.
- Godfrey, L. G. & Pesaran, M. H., 1983. "Tests of non-nested regression models: Small sample adjustments and Monte Carlo evidence," Journal of Econometrics, Elsevier, vol. 21(1), pages 133-154, January.
- Attfield, C. L. F., 1995. "A Bartlett adjustment to the likelihood ratio test for a system of equations," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 207-223.
- Godfrey, Leslie G, 1978. "Testing for Higher Order Serial Correlation in Regression Equations When the Regressors Include Lagged Dependent Variables," Econometrica, Econometric Society, vol. 46(6), pages 1303-10, November.
- Horowitz, J.L., 1995. "Bootstrap Methods in Econometrics: Theory and Numerical Performance," Working Papers 95-10, University of Iowa, Department of Economics.
- J. L. Horowitz, 1995. "Bootstrap Methods In Econometrics: Theory And Numerical Performance," SFB 373 Discussion Papers 1995,63, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
- Kiviet, Jan F, 1986. "On the Rigour of Some Misspecification Tests for Modelling Dynamic Relationships," Review of Economic Studies, Wiley Blackwell, vol. 53(2), pages 241-61, April.
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