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New estimators of the extreme value index under random right censoring, for heavy-tailed distributions

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Abstract

This paper presents new approaches for the estimation of the extreme value index in the framework of randomly censored samples, based on the ideas of Kaplan-Meier integration and the synthetic data approach of Leurgans (1987). These ideas are developed here in the heavy-tailed case, and lead to modifications of the Hill estimator, for which the consistency is proved under first order conditions. Simulations exhibit good performances of the two approaches, compared to the only existing adaptation of the Hill estimator in this context

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Correspondence to Rym Worms.

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Worms, J., Worms, R. New estimators of the extreme value index under random right censoring, for heavy-tailed distributions. Extremes 17, 337–358 (2014). https://doi.org/10.1007/s10687-014-0189-6

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Keywords

  • Extreme value index
  • Tail inference
  • Random censoring
  • Kaplan-Meier integration

Mathematical Subject Classifications

  • 62G32 (Extreme value statistics)
  • 62N02 (Estimation for censored data)