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A Parametric Bootstrap For Heavy-Tailed Distributions

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  • Cornea-Madeira, Adriana
  • Davidson, Russell

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.

Suggested Citation

  • Cornea-Madeira, Adriana & Davidson, Russell, 2015. "A Parametric Bootstrap For Heavy-Tailed Distributions," Econometric Theory, Cambridge University Press, vol. 31(3), pages 449-470, June.
    • Handle: RePEc:cup:etheor:v:31:y:2015:i:03:p:449-470_00
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    Cited by:

    1. Heiler, Phillip & Kazak, Ekaterina, 2021. "Valid inference for treatment effect parameters under irregular identification and many extreme propensity scores," Journal of Econometrics, Elsevier, vol. 222(2), pages 1083-1108.
    2. Giuseppe Cavaliere & S'ilvia Gonc{c}alves & Morten {O}rregaard Nielsen & Edoardo Zanelli, 2022. "Bootstrap inference in the presence of bias," Papers 2208.02028, arXiv.org, revised Nov 2023.
    3. Hill, Jonathan B. & Aguilar, Mike, 2013. "Moment condition tests for heavy tailed time series," Journal of Econometrics, Elsevier, vol. 172(2), pages 255-274.
    4. Trapani, Lorenzo, 2016. "Testing for (in)finite moments," Journal of Econometrics, Elsevier, vol. 191(1), pages 57-68.
    5. Li, Ming & Li, Jia-Yue, 2017. "Generalized Cauchy model of sea level fluctuations with long-range dependence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 484(C), pages 309-335.
    6. Daouia, Abdelaati & Stupfler, Gilles & Usseglio-Carleve, Antoine, 2023. "Bias-reduced and variance-corrected asymptotic Gaussian inference about extreme expectiles," TSE Working Papers 23-1444, Toulouse School of Economics (TSE), revised Nov 2023.
    7. Dewitte, Ruben, 2020. "From Heavy-Tailed Micro to Macro: on the characterization of firm-level heterogeneity and its aggregation properties," MPRA Paper 103170, University Library of Munich, Germany.

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