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A Lynden-Bell integral estimator for extremes of randomly truncated data

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  • Worms, J.
  • Worms, R.

Abstract

In the framework of heavy-tailed randomly truncated data, a new estimator is proposed for the extreme value index in a natural Lynden-Bell integral form. Extreme quantiles are also estimated, and the asymptotic normality is established under mild assumptions.

Suggested Citation

  • Worms, J. & Worms, R., 2016. "A Lynden-Bell integral estimator for extremes of randomly truncated data," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 106-117.
    • Handle: RePEc:eee:stapro:v:109:y:2016:i:c:p:106-117
    DOI: 10.1016/j.spl.2015.11.011
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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. 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.
    3. 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.
    4. Li, Yun-Xia & Wang, Jian-Feng, 2008. "An almost sure central limit theorem for products of sums under association," Statistics & Probability Letters, Elsevier, vol. 78(4), pages 367-375, March.
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    Cited by:

    1. Saida Mancer & Abdelhakim Necir & Souad Benchaira, 2023. "Bias Reduction in Kernel Tail Index Estimation for Randomly Truncated Pareto-Type Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1510-1547, August.
    2. Julien Worms & Rym Worms, 2018. "Extreme value statistics for censored data with heavy tails under competing risks," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(7), pages 849-889, October.
    3. 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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