A Refined Bootstrap For Heavy Tailed Distributions
AbstractIt is known that Efron's nonparametric bootstrap of the mean of random variables with common distribution in the domain of attraction of the stable laws 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 remedy for this problem, at least asymptomatically, is either the m out of n or the subsampling bootstrap. However, we show that both these bootstraps can be quite unreliable if the sample is not very large. A refined 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 refined 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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Bibliographic InfoPaper provided by McGill University, Department of Economics in its series Departmental Working Papers with number 2008-03.
Length: 22 pages
Date of creation: Aug 2008
Date of revision:
Find related papers by JEL classification:
- C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
- C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2008-08-06 (All new papers)
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