Multivariate parametric regression under shape constraints

François Wahl (1, 2) , Thibault Espinasse (2)

1 IFPEN - IFP Energies nouvelles
2 ICJ - Institut Camille Jordan

This paper first shows how to calculate a polynomial regression of any degree and of any number of variables under shape constraints. This framework is readily extended to linear combinations of basis functions as long as they respect a few key properties. It is proved that the procedure developed here is optimal in a certain sense. Theoretical explanations are first introduced for monotony constraints and then applied to simulated examples to show the behavior of the proposed algorithm. Two real industrial cases are then detailed and solved.

Mots clés: multivariate parametric regression; monotony; constraints; shape constraints; quadratic programming

Domaines: Statistiques [math.ST]

François Wahl, Thibault Espinasse. Multivariate parametric regression under shape constraints. 2016. ⟨hal-01262601v1⟩