A Parametric Bootstrap for Heavy Tailed Distributions

Adriana Cornea-Madeira and Russell Davidson

Post-Print from HAL

Abstract: It is known that Efron's bootstrap of the mean of a distribution in the domain of attraction of the stable laws with infinite variance is not consistent, in the sense that the limiting distribution of the bootstrap mean is not the same as the limiting distribution of the mean from the real sample. Moreover, the limiting bootstrap distribution is random and unknown. The conventional remedy for this problem, at least asymptotically, is either the m out of n bootstrap or subsampling. However, we show that both these procedures can be unreliable in other than very large samples. We introduce a parametric bootstrap that overcomes the failure of Efron's bootstrap and performs better than the m out of n bootstrap and subsampling. The quality of inference based on the parametric bootstrap is examined in a simulation study, and is found to be satisfactory with heavy-tailed distributions unless the tail index is close to 1 and the distribution is heavily skewed.

Keywords: Economie; quantitative (search for similar items in EconPapers)
Date: 2015-06
References: Add references at CitEc
Citations: View citations in EconPapers (4)

Published in Econometric Theory, 2015, 31 (03), pp.449--470. ⟨10.1017/S0266466614000395⟩

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
Journal Article: A PARAMETRIC BOOTSTRAP FOR HEAVY-TAILED DISTRIBUTIONS (2015)
Working Paper: A parametric bootstrap for heavytailed distributions (2009)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01456116

DOI: 10.1017/S0266466614000395

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().