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

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  • Mrkvicka, T.
  • Rataj, J.

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.

Suggested Citation

  • Mrkvicka, T. & Rataj, J., 2008. "On the estimation of intrinsic volume densities of stationary random closed sets," Stochastic Processes and their Applications, Elsevier, vol. 118(2), pages 213-231, February.
    • Handle: RePEc:eee:spapps:v:118:y:2008:i:2:p:213-231
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    References listed on IDEAS

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    1. Schmidt, Volker & Spodarev, Evgueni, 2005. "Joint estimators for the specific intrinsic volumes of stationary random sets," Stochastic Processes and their Applications, Elsevier, vol. 115(6), pages 959-981, June.
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    Cited by:

    1. Kateřina Staňková Helisová & Jakub Staněk, 2014. "Dimension Reduction in Extended Quermass-Interaction Process," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 355-368, June.
    2. Markéta Zikmundová & Kateřina Staňková Helisová & Viktor Beneš, 2014. "On the Use of Particle Markov Chain Monte Carlo in Parameter Estimation of Space-Time Interacting Discs," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 451-463, June.

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