Locally superoptimal and adaptive projection density estimators

We study a data-driven version of the density projection estimator in a general framework. We show that this estimator reaches a superoptimal rake on a dense set in the density class, and a quasi-optimal rake elsewhere. This set can be chosen by the statistician, and the superoptimal speed is reached for integrated quadratic error and almost sure uniform convergence. An adaptive version of the estimator is also considered.