Estimation of the Density Support and Its Functionals

We consider the recovering problem for the density support, i.e., the domain, where observable points are located. We study a nonparametric version of the problem; the asymptotics of the minimax risk as the number of observations tends to infinity is investigated. Together with the support restoring problem, we resolve an estimation problem for smooth functionals, for instance, the volume (area in the two-dimensional case) of the studied domain, the barycenter, etc. The asymptotic orders of the estimation precision are found and optimal estimates are obtained.