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Higher-Order Improvements of a Computationally Attractive-Step Bootstrap for Extremum Estimators

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Author Info
Donald W.K. Andrews () (Cowles Foundation, Yale University)

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Abstract

This paper establishes the higher-order equivalence of the k-step bootstrap, introduced recently by Davidson and MacKinnon (1999a), and the standard bootstrap. The k-step bootstrap is a very attractive alternative computationally to the standard bootstrap for statistics based on nonlinear extremum estimators, such as generalized method of moment and maximum likelihood estimators. The paper also extends results of Hall and Horowitz (1996) to provide new results regarding the higher-order improvements of the standard bootstrap and the k-step bootstrap for extremum estimators (compared to procedures based on first-order asymptotics). The results of the paper apply to Newton-Raphson (NR), default NR, line-search NR, and Gauss-Newton k-step bootstrap procedures. The results apply to the nonparametric iid bootstrap, non-overlapping and overlapping block bootstraps, and restricted and unrestricted parametric bootstraps. The results cover symmetric and equal-tailed two-sided t tests and confidence intervals, one-sided t tests and confidence intervals, Wald tests and confidence regions, and J tests of over-identifying restrictions. The optimal block length for the accuracy of tests and confidence intervals is shown to be proportional to N^{1/4} for both non-overlapping and overlapping block bootstraps in the context considered. In addition, the paper provides some results that establish the equivalence of the higher-order efficiency of non-bootstrap k-step statistics and extremum statistics. These results extend results of Pfanzagl (1974), Robinson (1988), and others.

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File URL: http://cowles.econ.yale.edu/P/cd/d12a/d1230.pdf
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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 1230.

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Length: 74 pages
Date of creation: Jul 1999
Date of revision:
Handle: RePEc:cwl:cwldpp:1230

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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
Fax: (203) 432-6167
Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Related research
Keywords: Asymptotics; block bootstrap; Edgeworth expansion; extremum estimator; Gauss-Newton; generalized method of moments estimator; higher-order efficiency; k-step bootstrap; maximum likelihood estimator; Newton-Raphson; parametric bootstrap; t statistic; test of over-identifying restrictions;

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  5. W. Härdle & J. Horowitz & J.-P. Kreiss, . "Bootstrap Methods For Time Series," Sonderforschungsbereich 373 2001-59, Humboldt Universitaet Berlin.
  6. Joseph P. Romano & Michael Wolf, 2002. "Improved Nonparametric Confidence Intervals in Time Series Regressions," Economics Working Papers 635, Department of Economics and Business, Universitat Pompeu Fabra. [Downloadable!]
  7. Valentina Corradi & Norman R. Swanson, 2003. "Bootstrap Conditional Distribution Tests In the Presence of Dynamic Misspecification," Departmental Working Papers 200311, Rutgers University, Department of Economics. [Downloadable!]
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  9. Wolfgang Keller, 2001. "The Geography and Channels of Diffusion at the World's Technology Frontier," NBER Working Papers 8150, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  10. Minford, Patrick & Theodoridis, Konstantinos & Meenagh, David, 2007. "Testing a model of the UK by the method of indirect inference," Cardiff Economics Working Papers E2007/2, Cardiff University, Cardiff Business School, Economics Section, revised Apr 2008. [Downloadable!]
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  11. Yuriy Gorodnichenko, 2005. "Reduced-Rank Identification of Structural Shocks in VARs," Macroeconomics 0512011, EconWPA. [Downloadable!]
  12. Keller, Wolfgang, 2001. "Knowledge Spillovers at the World's Technology Frontier," CEPR Discussion Papers 2815, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
  13. Sílvia Gonçalves & Halbert White, 2001. "The Bootstrap of the Mean for Dependent Heterogeneous Arrays," CIRANO Working Papers 2001s-19, CIRANO. [Downloadable!]
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  14. Keller, Wolfgang, 2001. "Geographic Localization of International Technology Diffusion," CEPR Discussion Papers 2706, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  15. Lutz Kilian & Atsushi Inoue, 2004. "Bagging Time Series Models," Econometric Society 2004 North American Summer Meetings 110, Econometric Society. [Downloadable!]
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  16. Aaron Mehrotra & Tuomas Peltonen & Alvaro Santos Rivera, 2007. "Modelling inflation in China - a regional perspective," Working Paper Series 829, European Central Bank. [Downloadable!]
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  17. Valentina Corradi & Norman Swanson, 2004. "Predective Density and Conditional Confidence Interval Accuracy Tests," Departmental Working Papers 200423, Rutgers University, Department of Economics. [Downloadable!]
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  18. Valentina Corradi & Norman Swanson, 2003. "The Block Bootstrap for Parameter Estimation Error In Recursive Estimation Schemes, With Applications to Predictive Evaluation," Departmental Working Papers 200313, Rutgers University, Department of Economics. [Downloadable!]
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