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Estimation of intrinsic volumes from parallel neighbourhoods. (English) Zbl 1101.62084

Gruber, Peter M. (ed.), Proceedings of the V. international conference of stochastic geometry, convex bodies, empirical measures and applications to engineering, medical and earth sciences, Mondello (Palermo), Italy, September 6–11, 2004. Palermo: Circolo Matemàtico di Palermo. Supplemento ai Rendiconti del Circolo Matemático di Palermo. Serie II 77, 553-563 (2006).
Let us consider a stationary random closed set in the Euclidean space. If it has locally positive reach then its intrinsic volume densities can be estimated from the Steiner formula, using the volumes of close parallel collars. A joint estimator of intrinsic volume densities of a stationary random closed set with values in the extended convex ring is proposed. It is based on approximations with parallel neighbourhoods, using the fact that the closures to the complements of these parallel neighbourhoods have locally positive reach.
For the entire collection see [Zbl 1091.52001].

MSC:

62M30 Inference from spatial processes
60D05 Geometric probability and stochastic geometry
62G05 Nonparametric estimation
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