Improving extreme quantile estimation via a folding procedure |
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Authors: | Alexandre You Ulrike Schneider Armelle Guillou Philippe Naveau |
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Institution: | 1. Université Paris VI, LSTA, Boîte 158, 175 rue du Chevaleret, 75013 Paris, France;2. University of Vienna, ISDS, Universitätsstr. 5, 1010 Wien, Austria;3. Institut de Recherche Mathématique Avancée UMR 7501, Université de Strasbourg et CNRS, 7 rue René-Descartes, 67084 Strasbourg cedex, France;4. Institute for Mathematical Stochastics, Georg-August-Universität, Goldschmidtstr. 7, D-037077 Göttingen, Germany |
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Abstract: | In many applications (geosciences, insurance, etc.), the peaks-over-thresholds (POT) approach is one of the most widely used methodology for extreme quantile inference. It mainly consists of approximating the distribution of exceedances above a high threshold by a generalized Pareto distribution (GPD). The number of exceedances which is used in the POT inference is often quite small and this leads typically to a high volatility of the estimates. Inspired by perfect sampling techniques used in simulation studies, we define a folding procedure that connects the lower and upper parts of a distribution. A new extreme quantile estimator motivated by this theoretical folding scheme is proposed and studied. Although the asymptotic behaviour of our new estimate is the same as the classical (non-folded) one, our folding procedure reduces significantly the mean squared error of the extreme quantile estimates for small and moderate samples. This is illustrated in the simulation study. We also apply our method to an insurance dataset. |
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Keywords: | Extreme quantile estimation Peaks-over-thresholds Generalized Pareto distribution Folding Generalized probability-weighted moments estimators |
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