  The paper deals with the density estimation on Rd under sup- norm loss. We
provide with fully data-driven estimation procedure and establish for it so
called sup-norm oracle inequality. The pro- posed estimator allows to take into
account not only approximation properties of the underlying density but
eventual independence struc- ture as well. Our results contain, as a particular
case, the complete solution of the bandwidth selection problem in multivariate
density model. Usefulness of the developed approach is illustrated by appli-
cation to adaptive estimation over anisotropic Nikolskii classes.
