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Name: Stefan Aulbach

Talk Title: Exceedance probability estimation – Some experience on bias correction and confidence intervals

Abstract: In applications, common tasks are to estimate the probability that a future observation will exceed a certain high threshold and, additionally, to state how “confident” one is in that estimate – expressed as a confidence interval. Particularly in the case that the threshold lies beyond the sample maximum, generalised Pareto distributions (GPDs) are a natural tool in the extrapolation of the probability in question. An advantage of a maximum likelihood estimation is that it can provide both quantities – the point estimate and the confidence interval – simultaneously, e.g., via the profile likelihood function. However, it is a common problem that, mostly due to the limited availability of data, a bias occurs in the estimation results. In this talk, we briefly revisit the analytical bias correction formulas for the GPD-parameters derived by Giles et al. (2016), which are based on results by Cox and Snell (1968) and Cordeiro and Klein (1994), and apply them in the estimation of the exceedance probability and the corresponding confidence bounds. Afterwards, we discuss the current state of a multivariate extension of the presented approach and compare two variants in the context of a bivariate logistic GPD model based on simulation results.

This talk is an invited talk at EVA 2021.