Limit theorems for Banach-valued autoregressive processes. Applications to real continuous time processes.
Asymptotic study of the density associated to a filter of infinite order. (Étude asymptotique de la densité associée à un filtre d'ordre infini.)
Estimation de la densité par projection sur un sous-espace de dimension finie
Lois limites et efficacité asymptotique des tests hilbertiens de dimension finie sous des hypothèses adjacentes
Étude d'une classe d'estimateurs non-paramétriques de la densité
Local superefficiency of data-driven projection density estimators in continuous time.
We construct a data-driven projection density estimator for continuous time processes. This estimator reaches superoptimal rates over a class F of densities that is dense in the family of all possible densities, and a «reasonable» rate elsewhere. The class F may be chosen previously by the analyst. Results apply to R-valued processes and to N-valued processes. In the particular case where square-integrable local time does exist, it is shown that our estimator is strictly better than the local time...
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