Estimating an endpoint with high order moments in the Weibull domain of attraction

Stéphane Girard; Armelle Guillou; Gilles Stupfler

hal-00648435, version 1

Estimating an endpoint with high order moments in the Weibull domain of attraction

Stéphane Girard ¹, Armelle Guillou ², Gilles Stupfler ³

Statistics and Probability Letters 82 (2012) 2136-2144

Abstract: We present a method for estimating the endpoint of a unidimensional sample when the distribution function belongs to the Weibull-max domain of attraction. The approach relies on transforming the variable of interest and then using high order moments of the positive variable obtained this way. It is assumed that the order of the moments goes to infinity. We give conditions on the rate of divergence to get the weak and strong consistency as well as the asymptotic normality of the estimator. The good performance of the estimator is illustrated on some finite sample situations.

1: MISTIS (INRIA Grenoble Rhône-Alpes / LJK Laboratoire Jean Kuntzmann)
INRIA – Laboratoire Jean Kuntzmann
2: Institut de Recherche Mathématique Avancée (IRMA)
CNRS : UMR7501 – Université de Strasbourg
3: Centre d'Études et de Recherche en Gestion d'Aix-Marseille (CERGAM)
Institut d'Administration des Entreprises (IAE) - Aix-en-Provence – Université Paul Cézanne - Aix-Marseille III : EA4225

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http://hal.archives-ouvertes.fr/hal-00648435
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From: Gilles Stupfler <>
Submitted on: Monday, 5 December 2011 16:53:32
Updated on: Friday, 30 November 2012 15:59:30

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