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Censoring estimators of a positive tail index

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  • Gomes, M. Ivette
  • Oliveira, Orlando

Abstract

In this paper, and in the context of regularly varying tails, we analyse some variants of a maximum likelihood estimator of a positive tail index [gamma], under a type II censoring scheme. These estimators are compared with the Hill estimator, for a Fréchet model and by means of a Monte Carlo simulation. Asymptotic normality of the estimators is derived, and a robustness simulation study of the estimators is undertaken.

Suggested Citation

  • Gomes, M. Ivette & Oliveira, Orlando, 2003. "Censoring estimators of a positive tail index," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 147-159, November.
    • Handle: RePEc:eee:stapro:v:65:y:2003:i:3:p:147-159
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    References listed on IDEAS

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    1. Drees, Holger & Kaufmann, Edgar, 1998. "Selecting the optimal sample fraction in univariate extreme value estimation," Stochastic Processes and their Applications, Elsevier, vol. 75(2), pages 149-172, July.
    2. L. De Haan & L. Peng, 1998. "Comparison of tail index estimators," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 52(1), pages 60-70, March.
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    Cited by:

    1. 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.

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