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