Estimation and uncertainty quantification for extreme quantile regions

Abstract

Estimation of extreme quantile regions, spaces in which future extreme events can occur with a given low probability, even beyond the range of the observed data, is an important task in the analysis of extremes. Existing methods to estimate such regions are available, but do not provide any measures of estimation uncertainty. We develop univariate and bivariate schemes for estimating extreme quantile regions under the Bayesian paradigm that outperforms existing approaches and provides natural measures of quantile region estimate uncertainty. We examine the method's performance in controlled simulation studies. We illustrate the applicability of the proposed method by analysing high bivariate quantiles for pairs of pollutants, conditionally on different temperature gradations, recorded in Milan, Italy.

A modeler's guide to extreme value software

“…The package also includes a procedure for computing pointwise confidence intervals using a nonparametric bootstrap. The UniExtQ from ExtremalDep provides credible intervals for bivariate extreme quantile regions (Beranger et al, 2021), estimated using an extension of this approach. Lastly, fCopulae provides parametric dependence function, correlation coefficient and tail dependence measures for bivariate extreme value copulas.…”

Reference Priors for the Generalized Extreme Value Distribution

“…This paper conducts an analogous investigation to Northrop and Attalides (2016), but with reference priors. Beranger et al (2019) focused on the estimation of returns levels in a Bayesian framework with the prior π(θ) ∝ 1/τ .…”

Estimating Concurrent Climate Extremes: A Conditional Approach

“…However, it is not sufficient to quantify concurrent extremes by conducting pairs of univariate analyses (i.e., only analyzing each variable separately) as by doing so could lead to under-or overestimation of risk if the variables of interest are respectively positively or negatively related to each other. There are relatively few climate studies considering extremes in a multivariate setting despite a large body of work in the statistical community having been dedicated to modeling multivariate and spatial extremes (Tawn, 1988(Tawn, , 1990Smith, 1990;Coles and Tawn, 1991;Tawn, 1996, 1997;Coles et al, 1999;Heffernan and Tawn, 2004;Cooley et al, 2006;Naveau et al, 2009;Davison et al, 2012;Wadsworth and Tawn, 2012a;Huser and Davison, 2014;Wadsworth and Tawn, 2018;Huang et al, 2019a;Wadsworth and Tawn, 2019;Huser and Wadsworth, 2019;Cooley et al, 2019;Beranger et al, 2019;Bopp et al, 2020). The existing methods for modeling multivariate (including spatial) extremes mostly focus on "component-wise extremes", in which extreme values for each component (e.g., climate variable) are first extracted separately and then combined to create a new extremal data vector.…”