Sharp adaptive estimation for d-dimensional classes

Karine Bertin (1)

1 Departamento de Estadistica [Valparaiso]

In this paper, our aim is to estimate an anisotropic function in the framework of the Gaussian white noise model. We suppose that the function belongs to an unknown d-dimensional Holder class. We evaluate the performance of an estimator by the sup-norm risk. We find the exact asymptotics of the adaptive minimax risk and construct asymptotically adaptive estimators.

Mots clés: anisotropic Holder class; minimax exact constant; uniform norm; white noise Model.; white noise Model

Domaines: Statistiques [math.ST]

Karine Bertin. Sharp adaptive estimation for d-dimensional classes. 2005. ⟨hal-00160734⟩