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

T. Mrkvicka and J. Rataj

Stochastic Processes and their Applications, 2008, vol. 118, issue 2, 213-231

Abstract: A new method of estimation of intrinsic volume densities for a stationary random closed set with values in the extended convex ring is introduced. The local Steiner formula is applied to the closure of the complement of the [epsilon]-parallel set to [Xi] for n>=d different radii and, by solving a linear regression model, estimates of the intrinsic volume densities of the [epsilon]-parallel set are obtained, which are used as approximations of the those of [Xi] itself. The consistency of the estimator as [epsilon]-->0 is shown, and the method is tested on simulations of a planar Boolean model of discs.

Keywords: Intrinsic; volumes; Random; closed; set; Positive; reach; Euler-Poincare; characteristic; Boolean; model (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (2)

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