Abstract
Let F be a distribution function in the domain of attraction of an extreme value distribution \(\mathcal{H}_{\gamma } \). In case γ ≥ 0 and F has an infinite end-point, we study the asymptotic behaviour of the relative approximation error \(\varepsilon _{\alpha } \) of a high quantile \(q_{\alpha } \) such that \(1 - F{\left( {q_{\alpha } } \right)} = \alpha \), where the order α tends to 0. We use the approximation of the excesses over a high threshold u by a Generalized Pareto distribution. We give sufficient conditions under which \(\varepsilon _{\alpha } \) tends to 0.
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AMS 2000 Subject Classification
Primary—60G70, Secondary—62G20, 62G32
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Beirlant, J., Raoult, JP. & Worms, R. On the Relative Approximation Error of the Generalized Pareto Approximation for a High Quantile. Extremes 6, 335–360 (2003). https://doi.org/10.1007/s10687-004-4724-0
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DOI: https://doi.org/10.1007/s10687-004-4724-0