Estimating an endpoint using high order moments

Stephane Girard 1 Armelle Guillou 2 Gilles Stupfler 2
1 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
Abstract : In 2008, Girard and Jacob presented a new method to estimate the frontier of a multidimensional sample. This method relies on a kernel regression on high order moments of the data, and was further used by the same authors to develop local polynomial estimators of a frontier. Using this approach, we present a new way to estimate the endpoint of a unidimensional sample when the distribution function belongs to the Weibull domain of attraction. The estimator is based on computing high order empirical moments of the variable of interest. Contrary to most popular methods, this one is not threshold-based. It is assumed that the order of the moments goes to infi nity, and provided a second-order assumption holds, we give conditions on its rate of divergence to get the asymptotic normality of the estimator. The good performance of the estimator is illustrated on some fi nite sample situations.
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Submitted on : Tuesday, July 23, 2013 - 10:40:11 PM
Last modification on : Wednesday, April 11, 2018 - 1:58:11 AM

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Stephane Girard, Armelle Guillou, Gilles Stupfler. Estimating an endpoint using high order moments. EVA 2011 - 7th International Conference on Extreme Value Analysis, Jun 2011, Lyon, France. ⟨hal-00847585⟩

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