On the estimation of intrinsic volume densities of stationary random closed sets

A new method of estimation of intrinsic volume densities for a stationary random closed set Ξ⊆RdΞ⊆Rd with values in the extended convex ring is introduced. The local Steiner formula is applied to the closure of the complement of the εε-parallel set to ΞΞ for n≥dn≥d different radii and, by solving a linear regression model, estimates of the intrinsic volume densities of the εε-parallel set are obtained, which are used as approximations of the those of ΞΞ itself. The consistency of the estimator as ε→0ε→0 is shown, and the method is tested on simulations of a planar Boolean model of discs.