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Asymptotically unbiased estimators for the extreme-value index

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  • Peng, L.

Abstract

Estimators of the extreme-value index are based on a set of upper order statistics. When the number of upper-order statistics used in the estimation of the extreme-value index is small, the variance of the estimator will be large. On the other hand, the use of a large number of upper statistics will introduce a big bias. There are several papers concerning how to balance the variance component and the bias component. In this paper, we give an unbiased estimator even if one uses a large number of upper-order statistics.

Suggested Citation

  • Peng, L., 1998. "Asymptotically unbiased estimators for the extreme-value index," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 107-115, June.
    • Handle: RePEc:eee:stapro:v:38:y:1998:i:2:p:107-115
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    References listed on IDEAS

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    1. Dekkers, A. L. M. & Dehaan, L., 1993. "Optimal Choice of Sample Fraction in Extreme-Value Estimation," Journal of Multivariate Analysis, Elsevier, vol. 47(2), pages 173-195, November.
    2. Laurens F.M. de Haan & Liang Peng & T.T. Pereira, 1997. "A Bootstrap-based Method to Achieve Optimality in Estimating the Extreme-value Index," Tinbergen Institute Discussion Papers 97-099/4, Tinbergen Institute.
    3. Hall, Peter, 1990. "Using the bootstrap to estimate mean squared error and select smoothing parameter in nonparametric problems," Journal of Multivariate Analysis, Elsevier, vol. 32(2), pages 177-203, February.
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    Cited by:

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    3. Igor Fedotenkov, 2020. "A Review of More than One Hundred Pareto-Tail Index Estimators," Statistica, Department of Statistics, University of Bologna, vol. 80(3), pages 245-299.
    4. Wager, Stefan, 2014. "Subsampling extremes: From block maxima to smooth tail estimation," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 335-353.
    5. Tsourti, Zoi & Panaretos, John, 2003. "Extreme Value Index Estimators and Smoothing Alternatives: A Critical Review," MPRA Paper 6390, University Library of Munich, Germany.
    6. Liu, Qing & Peng, Liang & Wang, Xing, 2017. "Haezendonck–Goovaerts risk measure with a heavy tailed loss," Insurance: Mathematics and Economics, Elsevier, vol. 76(C), pages 28-47.
    7. Gomes, M. Ivette & Brilhante, M. Fátima & Caeiro, Frederico & Pestana, Dinis, 2015. "A new partially reduced-bias mean-of-order p class of extreme value index estimators," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 223-237.
    8. M. Ivette Gomes & Armelle Guillou, 2015. "Extreme Value Theory and Statistics of Univariate Extremes: A Review," International Statistical Review, International Statistical Institute, vol. 83(2), pages 263-292, August.
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    14. Bucher, Axel & Segers, Johan, 2015. "Maximum likelihood estimation for the Frechet distribution based on block maxima extracted from a time series," LIDAM Discussion Papers ISBA 2015023, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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