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A Parametric Bootstrap for Heavy-Tailed Distributions

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JournalEconometric Theory
DateE-pub ahead of print - 8 Sep 2014
DatePublished (current) - 2015
Issue number5
Volume31
Pages (from-to)449-470
Early online date8/09/14
Original languageEnglish

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.

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