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04 - Ratio of Generalized Hill's estimator and its asymptotic normality ( Aliou Diop (Université de Saint-Louis, Sénégal))

3 avril 2009
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We present a statistical process depending on a continuous time parameter au whose each margin can arise a Generalized Hill's estimator. In this paper, the asymptotic normality of the
 nite-distributions of this family are completely characterized for
 au> 1/2 when the underlying distribution function lies on the maximum domain of attraction. The ratio of two different margins of the statistical process characterizes entirely the whole domain of attraction. Its asymptotic normality is also studied. The results permit in general to build a new family of estimators for the extreme value index whose asymptotic properties can be easily derived. For example, we give a new estimate of the Weibull extreme value index and we study its consistency and its asymptotic normality.

Travail joint avec Gane Samb Lo (Université de Saint-Louis, Sénégal).

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Durée : 52min


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