Deviation in kernel density estimation: super-optimal case

Corinne Berzin-Joseph (1)

1 LABSAD - Laboratoire de Statistiques et Analyse des Données

As in a previous Note [3] we study the asymptotic behaviour of several non-linear functionals of the empirical bridge in the super-optimal case. We consider the asymptotic behaviour of the number of crossings for the perturbed process in case the window satisfies $\sqrt{n}h^{2} \to +\infty$; applications of the asymptotics are found. We also obtain a central limit theorem for the integrated square error of density estimators and in general for a G-deviation in density estimation and for the Kullback deviation in the super-optimal case.

Domaines: Probabilités [math.PR]

Corinne Berzin-Joseph. Deviation in kernel density estimation: super-optimal case. Comptes Rendus de l'Académie des Sciences - Series I - Mathematics, 2000, 330 (9), pp.825-830. ⟨10.1016/S0764-4442(00)00271-8⟩. ⟨hal-00319336⟩