Exact adaptive pointwise estimation on Sobolev classes of densities

Abstract. The subject of this paper is to estimate adaptively the common probability density of n independent, identically distributed random variables. The estimation is done at a xed point x0 2 R, over the density functions that belong to the Sobolev class Wn (;L). We consider the adaptive problem setup, where the regularity parameter is unknown and varies in a given set Bn. A sharp adaptive estimator is obtained, and the explicit asymptotical constant, associated to its rate of convergence is found. Mathematics Subject Classication. 62N01, 62N02, 62G20