Benjamin Bobbia (université de Franche-Comté): Introduction to extreme quantile estimation and coupling methods for quantile regression

Séminaire double : Introduction to extreme quantile estimation and coupling methods for quantile regression

The extreme value theory is concerned by the behavior of tail distributions.
In this talk we seen first why we need a such theory and how we can use result about extremes to estimate extreme quantile.
That is quantile at un unobserved level.

Secondly, we will focus on the case of the estimation of conditional extreme quantiles. Namely the estimation of the quantile of a real velued random variable Y given a random variable in R^d.
In this purpose, we introduce the proportional tail model which assume that Y has an heavy tail with extreme value index 
and  that the conditional tail of Y given X=x is asymptotically proporional to the unconditional tail. 

We propose estimations of model parameters and of extreme quantiles as well as a validation procedure for this model. All these resultats are based on coupling approaches that we detail here.
Theses methods are based on the Wasserstien distances.