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Extreme value statistics for censored data with heavy tails under competing risks

Author

Listed:
  • Julien Worms

    (Université Paris-Saclay / Université de Versailles-Saint-Quentin-En-Yvelines, Laboratoire de Mathématiques de Versailles (CNRS UMR 8100))

  • Rym Worms

    (Université Paris-Est, Laboratoire d’Analyse et de Mathématiques Appliquées (CNRS UMR 8050))

Abstract

This paper addresses the problem of estimating, from randomly censored data subject to competing risks, the extreme value index of the (sub)-distribution function associated to one particular cause, in a heavy-tail framework. Asymptotic normality of the proposed estimator is established. This estimator has the form of an Aalen-Johansen integral and is the first estimator proposed in this context. Estimation of extreme quantiles of the cumulative incidence function is then addressed as a consequence. A small simulation study exhibits the performances for finite samples.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:81:y:2018:i:7:d:10.1007_s00184-018-0662-3
    DOI: 10.1007/s00184-018-0662-3
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    References listed on IDEAS

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    1. L. Peng & J. P. Fine, 2007. "Nonparametric quantile inference with competing–risks data," Biometrika, Biometrika Trust, vol. 94(3), pages 735-744.
    2. Ségolen Geffray, 2009. "Strong approximations for dependent competing risks with independent censoring," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(1), pages 76-95, May.
    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. Fermanian, Jean-David, 2003. "Nonparametric estimation of competing risks models with covariates," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 156-191, April.
    5. Jan Beyersmann & Martin Schumacher, 2008. "A note on nonparametric quantile inference for competing risks and more complex multistate models," Biometrika, Biometrika Trust, vol. 95(4), pages 1006-1008.
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    Cited by:

    1. Maeregu W. Arisido & Fulvia Mecatti & Paola Rebora, 2022. "Improving the causal treatment effect estimation with propensity scores by the bootstrap," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(3), pages 455-471, September.
    2. Liu, Bin & Shi, Yimin & Ng, Hon Keung Tony & Shang, Xiangwen, 2021. "Nonparametric Bayesian reliability analysis of masked data with dependent competing risks," Reliability Engineering and System Safety, Elsevier, vol. 210(C).

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