Author： Marohn F.
Publisher： Springer Publishing Company
ISSN： 0020-3157
Source： Annals of the Institute of Statistical Mathematics, Vol.49, Iss.4, 1997-12, pp. : 645-666
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Abstract
This paper deals with the estimation of the extreme value index in local extreme value models. We establish local asymptotic normality (LAN) under certain extreme value alternatives. It turns out that the central sequence occurring in the LAN expansion of the likelihood process is up to a rescaling procedure the Hill estimator. The central sequence plays a crucial role for the construction of asymptotic optimal statistical procedures. In particular, the Hill estimator is asymptotically minimax.
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