A local moment type estimator for an extreme quantile in regression with random covariates |
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Authors: | Yuri Goegebeur Armelle Guillou Michael Osmann |
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Affiliation: | 1. Department of Mathematics and Computer Science, University of Southern Denmark, Odense M, Denmark;2. Institut Recherche Mathématique Avancée, UMR 7501, Université de Strasbourg et CNRS, Strasbourg cedex, France |
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Abstract: | A conditional extreme quantile estimator is proposed in the presence of random covariates. It is based on an adaptation of the moment estimator introduced by Dekkers et al. (1989 Dekkers, A.L.M., Einmahl, J.H.J., de Haan, L. (1989). A moment estimator for the index of an extreme-value distribution. Ann. Statist. 17:1833–1855.[Crossref], [Web of Science ®] , [Google Scholar]) in the classical univariate setting, and thus it is valid in the domain of attraction of the extreme value distribution, i.e., whatever the sign of the extreme value index is. Asymptotic normality of the estimator is established under suitable assumptions, and its finite sample behavior is evaluated with a small simulation study, where a comparison with an alternative estimator already proposed in the literature is provided. An illustration to a real dataset concerning the world catalogue of earthquake magnitudes is also proposed. |
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Keywords: | Extreme quantile Local estimation Max-domain of attraction. |
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