Weiss-Hill estimator |
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| Authors: | M Isabel Fraga Alves |
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| Affiliation: | (1) Department of Statistics and Operations Research Faculty of Science, University of Lisbon, Portugal;(2) D.E.I.O. e C.E.A.U.L., C2, piso 2, Campo Grande, Faculdade de Ciências da Universidade de Lisboa, 1749-016 Lisboa, Portugal |
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| Abstract: | In this paper the asymptotic distributional behaviour is derived for a new estimator for the extreme value index γ of distribution,
which is a combination of two estimators proposed by Weiss and Hill (Weiss, 1971, and Hill, 1975). For |γ|>1/2, the estimator
outperforms the Moment estimator (Dekkers and al., 1989). in the sense that it has a smaller asymptotic variance than the
latter; moreover, for γ>1/2 (γ<0, resp.) the estimator behaves asymptoticaly like the Hillresp. Weiss—estimator; for |γ|<1/2
the estimator does not achieve the same rate of convergence as the Moment estimator. Simulation results concerning the comparison
of the mentioned estimators are also presented.
This research project was partially supported by FCT/PRAXIS XXI/FEDER and POCTI. |
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| Keywords: | Extreme value index extreme value theory mean squared error parameter estimation simulation |
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