Mean-of-order p reduced-bias extreme value index estimation under a third-order framework
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Reduced-bias versions of a very simple generalization of the ‘classical’ Hill estimator of a positive extreme value index (EVI) are put forward. The Hill estimator can be regarded as the logarithm of the mean-of-order-0 of a certain set of statistics. Instead of such a geometric mean, it is sensible to consider the mean-of-order-p (MOP) of those statistics, with p real. Under a third-order framework, the asymptotic behaviour of the MOP, optimal MOP and associated reduced-bias classes of EVI-estimators is derived. Information on the dominant non-null asymptotic bias is also provided so that we can deal with an asymptotic comparison at optimal levels of some of those classes. Large-scale Monte-Carlo simulation experiments are undertaken to provide finite sample comparisons.
KeywordsBias estimation Heavy tails Optimal levels Semi-parametric reduced-bias estimation Statistics of extremes
AMS 2000 Subject ClassificationsPrimary 62G32 Secondary 65C05
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- Brilhante, M.F., Gomes, M.I., Pestana, D.: The mean-of-order p extreme value index estimator revisited. In: Pacheco, A., et al (eds.) New Advances in Statistical Modeling and Application, pp 163–175. Springer, Berlin (2014)Google Scholar
- Caeiro, F., Gomes, M.I.: A semi-parametric estimator of a shape second order parameter. In: Pacheco, A., etal (eds.) New Advances in Statistical Modeling and Application, pp 163–175. Springer, Berlin (2014)Google Scholar
- Gomes, M.I., Henriques-Rodrigues, L., Manjunath, B.G.: Mean-of-order-p location-invariant extreme value index estimation. Revstat 14(3), 273–296 (2016b) Available at: https://www.ine.pt/revstat/pdf/PORT-MOPREVSTAT.pdf
- Reiss, R.-D., Thomas, M.: Statistical Analysis of Extreme Values, with Application to Insurance, Finance, Hydrology and Other Fields, 2nd edition; 3rd edition, Birkhäuser Verlag (2007)Google Scholar