A LASSO-type model for the bulk and tail of a heavy-tailed response

As widely known, in an extreme value framework, interest focuses on modelling the most extreme observations - disregarding the central part of the distribution; commonly, the effort centers on modelling the tail of the distribution by the generalized Pareto distribution, in a Peaks over threshold framework. Yet, in most practical situations it would be desirable to model both the bulk of the data along with the extreme values. In this talk, I will introduce a novel regression model for the bulk and the tail of a heavy-tailed response. Our regression model builds over the extended generalized Pareto distribution, as recently proposed by Naveau et al (2016). The proposed model allows us to learn the effect of covariates on a heavy-tailed response via a LASSO-type specification conducted via a Lagrangian restriction. The performance of the proposed approach will be assessed through a simulation study, and the method will be applied to a real data set.