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On the asymptotic normality of the extreme value index for right-truncated data

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  • Benchaira, Souad
  • Meraghni, Djamel
  • Necir, Abdelhakim

Abstract

Recently, Gardes and Stupfler (2015) introduced an estimator of the extreme value index under random truncation based on two distinct sample fractions of extremes from truncated and truncation data. In this paper, we make use of the weighted tail-copula processes to complete their work in the case of equal fractions.

Suggested Citation

  • Benchaira, Souad & Meraghni, Djamel & Necir, Abdelhakim, 2015. "On the asymptotic normality of the extreme value index for right-truncated data," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 378-384.
    • Handle: RePEc:eee:stapro:v:107:y:2015:i:c:p:378-384
    DOI: 10.1016/j.spl.2015.08.031
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    References listed on IDEAS

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    1. Laurent Gardes & Gilles Stupfler, 2015. "Estimating extreme quantiles under random truncation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 207-227, June.
    2. Drees, Holger & Huang, Xin, 1998. "Best Attainable Rates of Convergence for Estimators of the Stable Tail Dependence Function," Journal of Multivariate Analysis, Elsevier, vol. 64(1), pages 25-47, January.
    3. de Haan, Laurens & Neves, Cláudia & Peng, Liang, 2008. "Parametric tail copula estimation and model testing," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1260-1275, July.
    4. Einmahl, J.H.J. & de Haan, L.F.M. & Li, D., 2006. "Weighted approximations of tail copula processes with applications to testing the bivariate extreme value condition," Other publications TiSEM 18b65ac3-ba79-4bff-ad53-2, Tilburg University, School of Economics and Management.
    5. Laurent Gardes & Gilles Stupfler, 2015. "Erratum to: Estimating extreme quantiles under random truncation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 228-228, June.
    6. Laurent Gardes & Gilles Stupfler, 2015. "Estimating extreme quantiles under random truncation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 207-227, June.
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    Cited by:

    1. Benchaira, Souad & Meraghni, Djamel & Necir, Abdelhakim, 2016. "Kernel estimation of the tail index of a right-truncated Pareto-type distribution," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 186-193.

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