Least Squares estimation of two ordered monotone regression curves

Fadoua Balabdaoui (1) , Kaspar Rufibach (2) , Filippo Santambrogio (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 institut für Sozial-und Präventivmedizin

To project (in the L2 metric) a single function f on the set of increasing functions one takes the primitive of f, then its convex hull, and then takes the derivative. Here the problem is more complicated: project a pair (f,g) on the set of pairs of increasing functions, the former smaller than the latter. It is a regression problem with applications in statistics. The solution is not explicit but we solve it numerically through a projected subgradient algorithm from convex optimization

Domaines: Statistiques [math.ST]; Théorie [stat.TH]; Optimisation et contrôle [math.OC]

Fadoua Balabdaoui, Kaspar Rufibach, Filippo Santambrogio. Least Squares estimation of two ordered monotone regression curves. 2009. ⟨hal-00417281⟩