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Wild Bootstrap of the Sample Mean in the Infinite Variance Case

Author

Listed:
  • Giuseppe Cavaliere
  • Iliyan Georgiev
  • A. M. Robert Taylor

Abstract

It is well known that the standard independent, identically distributed (iid) bootstrap of the mean is inconsistent in a location model with infinite variance (α-stable) innovations. This occurs because the bootstrap distribution of a normalised sum of infinite variance random variables tends to a random distribution. Consistent bootstrap algorithms based on subsampling methods have been proposed but have the drawback that they deliver much wider confidence sets than those generated by the iid bootstrap owing to the fact that they eliminate the dependence of the bootstrap distribution on the sample extremes. In this paper we propose sufficient conditions that allow a simple modification of the bootstrap (Wu, 1986) to be consistent (in a conditional sense) yet to also reproduce the narrower confidence sets of the iid bootstrap. Numerical results demonstrate that our proposed bootstrap method works very well in practice delivering coverage rates very close to the nominal level and significantly narrower confidence sets than other consistent methods.

Suggested Citation

  • Giuseppe Cavaliere & Iliyan Georgiev & A. M. Robert Taylor, 2013. "Wild Bootstrap of the Sample Mean in the Infinite Variance Case," Econometric Reviews, Taylor & Francis Journals, vol. 32(2), pages 204-219, February.
  • Handle: RePEc:taf:emetrv:v:32:y:2013:i:2:p:204-219
    DOI: 10.1080/07474938.2012.690660
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    File URL: http://hdl.handle.net/10.1080/07474938.2012.690660
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    Cited by:

    1. Eric Beutner & Alexander Heinemann & Stephan Smeekes, 2017. "A Justification of Conditional Confidence Intervals," Papers 1710.00643, arXiv.org.

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