Minimax exact constant in sup-norm for nonparametric regression with random design

Karine Bertin (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We consider the nonparametric regression model with random design. We study the estimation of a regression function f in the uniform norm assuming that f belongs to a Holder class. We determine the minimax exact constant and an asymptotically exact estimator. They depend on the minimum value of the design density.

Mots clés: nonparametric regression; minimax risk; minimax exact constant; uniform norm

Domaines: Statistiques [math.ST]

Karine Bertin. Minimax exact constant in sup-norm for nonparametric regression with random design. 2004. ⟨hal-00007738⟩