Estimation adaptative de la densité avec données échantillonnées

Abstract

In continuous time, rates of convergence for nonparametric density estimators depend on the nature of sample paths: roughly speaking, the more ‘irregular’ the paths are, the better the rates are. In this framework, we give the pointwise rate of convergence of the kernel density estimator in the case of sampled observations. Behaviour of the estimator depends on two coefficients r 0, γ 0 respectively linked with regularity of density and regularity of sample paths. We propose an adaptive estimator relatively to γ 0 as well as a doubly adaptive estimator (with respect to r 0 and γ 0). It is shown that the rate of convergence obtained in the case of known r 0, γ 0 is achieved by such adaptive estimators. To cite this article: D. Blanke, C. R. Acad. Sci. Paris, Ser. I 337 (2003).