A parametric bootstrap for heavytailed distributionsAdriana Cornea-Madeira and Russell Davidson Working Papers from HAL Abstract: It is known that Efron's resampling bootstrap of the mean of random variables with common 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 distribution of the bootstrap mean 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 quite unreliable in other than very large samples. A parametric bootstrap is derived by considering the distribution of the bootstrap P value instead of that of the bootstrap statistic. 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: bootstrap inconsistency; stable distribution; domain of attraction; infinite variance (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:hal:wpaper:halshs-00443564 Access Statistics for this paper More papers in Working Papers from HAL |
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