Skip to main content
Log in

Implementing the single bootstrap: Some computational considerations

  • Published:
Computational Economics Aims and scope Submit manuscript

Abstract

In applied econometrics, the researcher typically has two recourses for conducting inference: assuming normal errors or relying on asymptotic theory. In economic models, the assumption of normal errors is rarely justified and, for moderate sample sizes, the applicability of a central limit theorem is questionable. Researchers now have a third alternative: the bootstrap. Central to the bootstrap methodology is the idea that computational force can substitute for theoretical analysis. This article explains the bootstrap method, shows how a simple transformation can improve the reliability of inference, gives an algorithm for bootstrapping a regression equation, and discusses some computational pitfalls.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Beran, R., 1987, Prepivoting to reduce level error of confidence sets,Biometrika 74, 457–468.

    Google Scholar 

  • Beran, R., 1988a, Prepivoting test statistics: a bootstrap view of asymptotic refinements,J. Am. Stat. Assoc. 83, 687–697.

    Google Scholar 

  • Beran, R., 1988b, Comment on a paper by Hall,Ann. Stat. 16, 956–959.

    Google Scholar 

  • Beran, R., 1990, Refining bootstrap simultaneous confidence sets,J. Am. Stat. Assoc. 85, 417–426.

    Google Scholar 

  • Brownstone, D., 1990, Bootstrapping improved estimators for linear regression models,J. Econometrics 44, 171–187.

    Google Scholar 

  • Doan, T., 1990,User's Manual, RATS v. 3.10 (Regression Analysis for Time Series), VAR Econometrics, Evanston, Ill.

  • Efron, B., 1979, Bootstrap methods: another look at the jackknife,Ann. Stat. 7, 1–26.

    Google Scholar 

  • Efron, B., 1980, Censored data and the bootstrap,J. Am. Stat. Assoc. 76, 312–319.

    Google Scholar 

  • Efron, B., 1981, Nonparametric standard errors and confidence intervals (with discussion),Canad. J. Stat. 9, 139–172.

    Google Scholar 

  • Efron, B., 1982,The Jackknife, Bootstrap, and Other Resampling Plans, CBMS-NSF Monographs, 38, SIAM, Philadelphia.

    Google Scholar 

  • Efron, B., 1987, Better bootstrap confidence intervals and approximations,J. Am. Stat. Assoc. 82, 171–185.

    Google Scholar 

  • Efron, B., 1990, More efficient bootstrap computations,J. Am. Stat. Assoc. 82, 171–185.

    Google Scholar 

  • Efron, B., and Tibshirani, R., 1986, Bootstrap methods of standard errors, confidence intervals, and other measures of statistical accuracy,Stat. Sci. 1, 54–75.

    Google Scholar 

  • Fisher, I., 1930,The Theory of Interest, MacMillan, New York.

    Google Scholar 

  • Freedman, D. and Peters, S., 1984, Bootstrapping a regression equation: Some empirical results,J. Am. Stat. Assoc. 79, 97–106.

    Google Scholar 

  • Hall, P., 1988, Theoretical comparison of bootstrap confidence intervals,Ann. Stat. 16, 927–953.

    Google Scholar 

  • Hall, P. and Martin M., 1988, On bootstrap resampling and iteration,Biometrika,75, 661–671.

    Google Scholar 

  • Hinkley, D. and Wei, B.C., 1984, Improvement of jackknife confidence limit methods,Biometrika 71, 331–339.

    Google Scholar 

  • Kendall, M.G. and Stuart A., 1977,The Advanced Theory of Statistics, 4e, vol. 1, Griffin, London.

    Google Scholar 

  • McCullough, B.D., 1991, Bootstrapping a regression equation: an application to Fisher's Equation, paper, presented at the Statistics '91 Canada: Third Conference on Applied Statistics, Montreal.

  • Mood, A, Graybill F., and Boes, D., 1974,Introduction to the Theory of Statistics, McGraw-Hill, New York.

    Google Scholar 

  • Press, W., Flannery B., Teukolsky, S., and Vetterlin, W., 1986,Numerical Recipes: The Art of Scientific Computing. Cambridge University Press, Cambridge.

    Google Scholar 

  • Quenouille, M., 1949, Approximate tests of correlation in time series,J. Roy. Stat. Soc., Ser. B 11, 18–84.

    Google Scholar 

  • Singh, K., 1981, On the asymptotic accuracy of Efron's bootstrap,Ann. Stat. 9, 1187–1195.

    Google Scholar 

  • Tukey, J., 1977,Exploratory Data Analysis, Addison-Wesley, Reading, Mass.

    Google Scholar 

  • Velleman, P.F. and Hoaglin, D.C., 1981,Applications, Basics, and Computing of Exploratory Data Analysis, Duxbury, Boston.

    Google Scholar 

  • Vinod, H.D., 1992, Bootstrap, jackknife resampling and simulation mnethods: applications in econometrics, in C.R. Rao, G.S. Maddala, and H.D. Vinod, (eds),Handbook of Statistics: Econometrics, (to appear).

  • Vinod, H. and McCullough, B.D., 1991, Estimating cointegrating parameters: an application of the double bootstrap, paper, presented at the Statistics '91 Canada: Third Conference on Applied Statistics, Montreal.

  • Vinod, H. and Raj B., 1988, Economic issues in the Bell System divestiture: a bootstrap application,J. Roy. Stat. Soc. C 37, 251–261.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

McCullough, B.D., Vinod, H. Implementing the single bootstrap: Some computational considerations. Comput Econ 6, 1–15 (1993). https://doi.org/10.1007/BF01885372

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01885372

Key words

Navigation