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Estimating extreme quantiles under random truncation

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  • Laurent Gardes
  • Gilles Stupfler

Abstract

The goal of this paper is to provide estimators of the tail index and extreme quantiles of a heavy-tailed random variable when it is right truncated. The weak consistency and asymptotic normality of the estimators are established. The finite sample performance of our estimators is illustrated on a simulation study and we showcase our estimators on a real set of failure data. Copyright Sociedad de Estadística e Investigación Operativa 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:24:y:2015:i:2:p:207-227
    DOI: 10.1007/s11749-014-0403-5
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    References listed on IDEAS

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    1. Kaminsky, Kenneth S., 1987. "Prediction of IBNR claim counts by modelling the distribution of report lags," Insurance: Mathematics and Economics, Elsevier, vol. 6(2), pages 151-159, April.
    2. Herbst, Tomas, 1999. "An application of randomly truncated data models in reserving IBNR claims," Insurance: Mathematics and Economics, Elsevier, vol. 25(2), pages 123-131, November.
    3. 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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    Citations

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    Cited by:

    1. Takeshi Emura & Chi-Hung Pan, 2020. "Parametric likelihood inference and goodness-of-fit for dependently left-truncated data, a copula-based approach," Statistical Papers, Springer, vol. 61(1), pages 479-501, February.
    2. 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.
    3. 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.
    4. Stupfler, Gilles, 2016. "Estimating the conditional extreme-value index under random right-censoring," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 1-24.
    5. 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.
    6. 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.
    7. Laurent Gardes & Stéphane Girard & Gilles Stupfler, 2020. "Beyond tail median and conditional tail expectation: Extreme risk estimation using tail Lp‐optimization," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 922-949, September.

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