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arXiv · 1905.08726

L-moments for automatic threshold selection in extreme value analysis

Jessica Silva Lomba·Maria Isabel Fraga Alves
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Abstract

In extreme value analysis, sensitivity of inference to the definition of extreme event is a paramount issue. Under the peaks-over-threshold (POT) approach, this translates directly into the need of fitting a Generalized Pareto distribution to observations above a suitable level that balances bias versus variance of estimates. Selection methodologies established in the literature face recurrent challenges such as an inherent subjectivity or high computational intensity. We suggest a truly automated method for threshold detection, aiming at time efficiency and elimination of subjective judgment. Based on the well-established theory of L-moments, this versatile data-driven technique can handle batch processing of large collections of extremes data, while also presenting good performance on small samples. The technique's performance is evaluated in a large simulation study and illustrated with significant wave height data sets from the literature. We find that it compares favorably to other state-of-the-art methods regarding the choice of threshold, associated parameter estimation and the ultimate goal of computationally efficient return level estimation.

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Jessica Silva Lomba, Maria Isabel Fraga Alves. 2019-05-21. L-moments for automatic threshold selection in extreme value analysis. https://doi.org/10.1007/s00477-020-01789-x

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