Monday, July 1, 2013

The Bootstrap - A Non-Technical Introduction

Computer-intensive methods have become essential to much of statistical analysis, and that includes econometrics. Think of Monte Carlo simulations, MCMC for Bayesian methods, maximum simulated likelihood, empirical likelihood methods, the jackknife, and (of course) the bootstrap.

Although we usually date the bootstrap from Bradley Efron's 1979 paper, as a resampling method it has its roots in earlier, related, contributions including those of Quenouille (1949, 1956).

The main purpose of this post is to draw readers' attention to the piece by Diaconis and Efron (1983) that appeared in Scientific American. It's written for a "general audience", which is nice, and it also provides an interesting snapshot of what was cutting-edge computing 30 years ago. The discussion paper version of the article (including typos) is available here.

As a final bonus, the examples include one from econometrics!


References

Diaconis and B. Efron, 1983. Computer intensive methods in statistics. Scientific American, 248, 116-132.

Efron, B., 1979. Bootstrap methods: Another look at the jackknife. Annals of Statistics, 7, 1-26.

Quenouille, M. H.,1949. Approximate tests of correlation in time series. Journal of the Royal
Statistical Society, Series B, 11, 18-44.

Quenouille, M. H.,1956. Notes on bias in estimation. Biometrika, 61, 353-360.


© 2013, David E. Giles

3 comments:

  1. Could you recommend a reference for a time series bootstrap? I found the recommended procedure at the end of http://robjhyndman.com/hyndsight/crossvalidation/ puzzling.

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    Replies
    1. Dimitriy - the "block bootstrap" is commonly used for time-series. For example, see Hardle et al., http://pareto.uab.es/mcreel/reading_course_2005_2006/HardleHorowitzKreiss.pdf

      If you're bootstrapping unit root tests, then special care is needed. See Maddala and Kim's book, "Unit Roots, Cointegration, and Structural Change".

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  2. Thank you! That looks like a very useful reference.

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