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Second-order refined peaks-over-threshold modelling for heavy-tailed distributions. (English) Zbl 1162.62044
Summary: Modelling excesses over a high threshold using the Pareto or generalized Pareto distribution (PD/GPD) is the most popular approach in extreme value statistics. This method typically requires high thresholds in order for the (G)PD to fit well and in such a case applies only to a small upper fraction of the data. The extension of the (G)PD proposed in this paper is able to describe the excess distribution for lower thresholds in case of heavy-tailed distributions. This yields a statistical model that can be fitted to a larger portion of the data. Moreover, estimates of the tail parameters display the stability for a larger range of thresholds. Our findings are supported by asymptotic results, simulations and a case study.

MSC:
62G32Statistics of extreme values; tail inference
62G05Nonparametric estimation
62G20Nonparametric asymptotic efficiency
65C60Computational problems in statistics
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