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

Stéphane Girard 1 Armelle Guillou 2 Gilles Stupfler 3
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, Grenoble INP - Institut polytechnique de Grenoble - Grenoble Institute of Technology
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.
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Submitted on : Friday, November 30, 2012 - 4:12:02 PM
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Stéphane Girard, Armelle Guillou, Gilles Stupfler. Estimating an endpoint with high order moments in the Weibull domain of attraction. Statistics and Probability Letters, Elsevier, 2012, 82 (12), pp.2136-2144. ⟨10.1016/j.spl.2012.07.005⟩. ⟨hal-00648435v2⟩

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