Exact adaptive pointwise estimation on Sobolev classes of densities
The subject of this paper is to estimate adaptively the common probability density of independent, identically distributed random variables. The estimation is done at a fixed point , over the density functions that belong to the Sobolev class . We consider the adaptive problem setup, where the regularity parameter is unknown and varies in a given set . A sharp adaptive estimator is obtained, and the explicit asymptotical constant, associated to its rate of convergence is found.