Within the general aim of extreme value statistics lies the estimation of an event that is so rare that might have never been witnessed in the past. Whilst the parametric estimation of an extreme quantile has found its way to the lore of many applied sciences, in terms of evaluating return levels, analogous non-parametric methodology is far less explored. This is an interesting topic because there are different albeit equivalent ways to define an (extreme) out-of-sample quantile as underpinned by different constructs arising from the same foundational extreme value theorem.

In this talk, I will address two of these definitions through the domains of attraction framework and will explain how we succeeded in generalising one of them to allow for either cases of finite or infinite upper bound to the distribution underlying the sampled data.