The Power of Bootstrap and Asymptotic Tests
AbstractWe 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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Bibliographic InfoPaper provided by Queen's University, Department of Economics in its series Working Papers with number 1035.
Length: 22 pages
Date of creation: Jul 2004
Date of revision:
Publication status: Forthcoming in Journal of Econometrics
bootstrap test; bootstrap discrepancy; Pitman drift; drifting DGP; Monte Carlo; test power; power; asymptotic test;
Other versions of this item:
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2006-03-11 (All new papers)
- NEP-ECM-2006-03-11 (Econometrics)
- NEP-ETS-2006-03-11 (Econometric Time Series)
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- Russell Davidson & James G. MacKinnon, 2001.
"Bootstrap Tests: How Many Bootstraps?,"
1036, Queen's University, Department of Economics.
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"Convenient specification tests for logit and probit models,"
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- Russell Davidson & James G. MacKinnon, 1994.
"Graphical Methods for Investigating the Size and Power of Hypothesis Tests,"
903, Queen's University, Department of Economics.
- 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, 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).
- Rudolf Beran, 1997. "Diagnosing Bootstrap Success," Annals of the Institute of Statistical Mathematics, Springer, 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.
- Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, September.
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