Deviation in kernel density estimation: super-optimal case

International audienceAs 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