Extreme value theory (EVT) is the branch of Statistics concerned with extremes or tails of a distribution. It has a long list of areas of application, including Finance and Environmental Sciences. One of the main concerns of EVT is to model exceedances, or values beyond a sufficiently high quantile. Nice theoretical results suggest the way forward to approximate exceedance behaviour, but do not define how extreme one needs to be for the approximation to work well. Ad-hoc procedures are commonly used to address this issue but they suffer from the pitfalls inherent to such procedures and do not take into account the uncertainty associated. Thus, resulting inference is likely to be biased and/or to underestimate uncertainty. We propose a procedure that avoids such pitfalls by letting the data drive the decision of when the approximation can be safely applied, while accounting for the uncertainty of this choice. The procedures are extended to: 1) accommodate for the inclusion of external sources of information; 2) the time series context to incorporate temporal dependence; 3) identify the extremal behavior, and; 4) handle multivariate contexts.
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Dani Gamerman is a Visiting Professor at UFMG since 2019. Professor (1996 to 2019) and Emeritus (2021) at UFRJ. He is the author of the books Monte Carlo Markov Chain: Stochastic Simulation for Bayesian Inference (Chapman & Hall, 2006, 2nd edition) and Statistical Inference: an Integrated Approach, with Helio S. Migon and Francisco Louzada (Chapman & Hall, 2014, 2a. edition), in addition to national books. He has published articles in several statistical journals such as Journal of the Royal Statistical Society Series B, Biometrika, Applied Statistics, Statistics & Computing and Journal of Multivariate Analysis. His research activities include dynamic models, spatial statistics, survival analysis, extreme value theory, IRT, stochastic simulation and Bayesian inference.