In "A local nearest-neighbor convex-hull construction of home ranges and utilization distributions" authors proposed an algorithm for "home ranges" and "utilization distributions" that can be translated into statistics as support and density estimation.
In a first part we give the properties of the associated support estimator when the support is "full dimensional" but also when the support is a lower dimensional manifold (with or without boundary).
A second part is dedicated to the density (and level set) estimation. When applying the local convex hull idea for that purpose the initial estimator is biased and this bias can be reduced. We will present the bias reduction method and show that it allows to have density estimator adapted to (unknown) compact support. An extension of the proposed estimator when the distribution is supported by a  (unknown) lower dimensional manifold with or without boundary is also given.