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Consistent estimation of the tail index for dependent data

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  • Brito, Margarida
  • Freitas, Ana Cristina Moreira

Abstract

We consider the estimation of the tail-index for dependent random variables. We establish the consistency of the geometric-type estimator (Brito and Freitas, 2003) for stationary sequences satisfying general mixing conditions and derive a simplified condition, specially adapted for applications.

Suggested Citation

  • Brito, Margarida & Freitas, Ana Cristina Moreira, 2010. "Consistent estimation of the tail index for dependent data," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1835-1843, December.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:23-24:p:1835-1843
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    References listed on IDEAS

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    1. Jon Danielsson & Casper G. de Vries, 1998. "Beyond the Sample: Extreme Quantile and Probability Estimation," FMG Discussion Papers dp298, Financial Markets Group.
    2. Brito, Margarida & Moreira Freitas, Ana Cristina, 2003. "Limiting behaviour of a geometric-type estimator for tail indices," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 211-226, October.
    3. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
    4. Schultze J. & Steinebach J., 1996. "On Least Squares Estimates Of An Exponential Tail Coefficient," Statistics & Risk Modeling, De Gruyter, vol. 14(4), pages 353-372, April.
    5. Brito, Margarida & Moreira Freitas, Ana Cristina, 2006. "Weak convergence of a bootstrap geometric-type estimator with applications to risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 38(3), pages 571-584, June.
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