Estimating the density support and its functionals

The problem of the density support reconstruction is dealt with. The density support is a region where the observation points are distributed. The problem is set up in the non-parametric form. The asymptotics of minimax risk is considered under the nonlimited increase of the number of observations. Along with the problem of the density support reconstruction the problem of estimation of smooth functionals is studied. The smooth functionals, as for instance, the volume (the surface in a two-dimensional case) of the sought-for region, its gravity centre, etc. Asymptotic orders of estimation accuracy are found and optimal estimates are constructed.