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A new partially reduced-bias mean-of-order p class of extreme value index estimators

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  • Gomes, M. Ivette
  • Brilhante, M. Fátima
  • Caeiro, Frederico
  • Pestana, Dinis

Abstract

A class of partially reduced-bias estimators of a positive extreme value index (EVI), related to a mean-of-order-p class of EVI-estimators, is introduced and studied both asymptotically and for finite samples through a Monte-Carlo simulation study. A comparison between this class and a representative class of minimum-variance reduced-bias (MVRB) EVI-estimators is further considered. The MVRB EVI-estimators are related to a direct removal of the dominant component of the bias of a classical estimator of a positive EVI, the Hill estimator, attaining as well minimal asymptotic variance. Heuristic choices for the tuning parameters p and k, the number of top order statistics used in the estimation, are put forward, and applied to simulated and real data.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:82:y:2015:i:c:p:223-237
    DOI: 10.1016/j.csda.2014.08.017
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    References listed on IDEAS

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    1. Peng, L., 1998. "Asymptotically unbiased estimators for the extreme-value index," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 107-115, June.
    2. Gomes, M. Ivette & Pestana, Dinis, 2007. "A Sturdy Reduced-Bias Extreme Quantile (VaR) Estimator," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 280-292, March.
    3. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
    4. M. Ivette Gomes & Laurens De Haan & Lígia Henriques Rodrigues, 2008. "Tail index estimation for heavy‐tailed models: accommodation of bias in weighted log‐excesses," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 31-52, February.
    5. Frederico Caeiro & M. Ivette Gomes, 2011. "Asymptotic comparison at optimal levels of reduced‐bias extreme value index estimators," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 65(4), pages 462-488, November.
    6. Fátima Brilhante, M. & Ivette Gomes, M. & Pestana, Dinis, 2013. "A simple generalisation of the Hill estimator," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 518-535.
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    1. Chen, Yu & Ma, Mengyuan & Sun, Hongfang, 2023. "Statistical inference for extreme extremile in heavy-tailed heteroscedastic regression model," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 142-162.

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