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Bias Reduction in Kernel Tail Index Estimation for Randomly Truncated Pareto-Type Data

Author

Listed:
  • Saida Mancer

    (Mohamed Khider University of Biskra)

  • Abdelhakim Necir

    (Mohamed Khider University of Biskra)

  • Souad Benchaira

    (Mohamed Khider University of Biskra)

Abstract

A bias reduction to a kernel estimator of the tail index of randomly right-truncated Pareto-type distributions is made. The asymptotic normality of the derived estimator is established by assuming the second-order condition of regular variation. A simulation study is carried out to evaluate the finite sample behavior of the proposed estimator and compare it to those with non-reduced bias. An application to a real dataset of lifetimes of automobile brake pads is done.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sankha:v:85:y:2023:i:2:d:10.1007_s13171-022-00303-5
    DOI: 10.1007/s13171-022-00303-5
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    References listed on IDEAS

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    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.
    2. 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.
    3. 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.
    4. Beirlant, J. & Maribe, G. & Verster, A., 2018. "Penalized bias reduction in extreme value estimation for censored Pareto-type data, and long-tailed insurance applications," Insurance: Mathematics and Economics, Elsevier, vol. 78(C), pages 114-122.
    5. Strzalkowska-Kominiak, E. & Stute, W., 2009. "Martingale representations of the Lynden-Bell estimator with applications," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 814-820, March.
    6. Beirlant, J. & Bardoutsos, A. & de Wet, T. & Gijbels, I., 2016. "Bias reduced tail estimation for censored Pareto type distributions," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 78-88.
    7. 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.
    8. 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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