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Introduction to extreme values theory and extreme quantile estimation

par Bobbia Benjamin - publié le

Benjamin Bobbia
(Université de Bourgogne-Franche-Comté, Besançon)

Whereas the normal theory of statistics is focused on a behavior of the mean of an sample, the extreme value theory is interested in the behavior of the maximum (or minimum) of a sample. The purpose is to identified when rare event will happened and how catastrophic they can be. There are two approaches, the peak over threshold (POT) and the block maxima (BM). I propose, in this talk, to have a quick overview of these two methods and to see some of the most important theorem. And also how we can estimate an extreme quantile, which is a quantile at an unobserved level.

Moreover, we address the problem of the generalization of quantile estimation to a more general framework of regression.