Multivariate parametric regression under shape constraints

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

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

We consider a multivariate regression model built as a linear combination of functions of a single variable in univariate situations, or of product of univariate functions in multivariate cases. For each variable, the univariate functions form a Chebyshev system. The regression model is defined on a bounded domain and subject to one or more shape constraints on its definition domain, with the restriction that they can be transformed in positivity constraints for the regression function itself or for its derivatives. We develop an iterative procedure, where at each step the initial shape requirement is approximated by a set of linear constraints. This procedure is shown to converge to the optimal solution in the least square sense for univariate and then for multivariate cases. Numerical studies and a real industrial example with a multivariate polynomial regression subject to shape constraints of monotony illustrate the performance of the proposed method.

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

Domaines: Statistiques [math.ST]

François Wahl, Thibault Espinasse. Multivariate parametric regression under shape constraints. 2017. ⟨hal-01262601v2⟩