L-functionals and regression models

[jorenham]

Hössjer & Karlsson (2023) describe the framework of L-functionals, which (almost) generalize the Legendre-based (untrimmed) L-moments. They additionally re-invent Hyowon An's Gaussian-centered "HL-moments", and dub them "Hermite L-functionals". Similarly, they introduce the (novel) Laguerre L-functionals with Exp(1) as reference distribution, which sound rather promising IMHO.

They further show how to apply these L-functionals for regression in (transformed) linear- and quantile-regression models (!), using a very flexible, yet practical approach.

Their use of conditional L-functionals might be interesting to attempt to "backport" into the familiar (Legendre- & Jacobi-based) L-moments.

For now, more research into these L-functionals is required before coming up with a concrete implementation plan.