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...