IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v118y2008i2p213-231.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(07)00057-9
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. David Dereudre & Frédéric Lavancier & Kateřina Staňková Helisová, 2014. "Estimation of the Intensity Parameter of the Germ-Grain Quermass-Interaction Model when the Number of Germs is not Observed," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 809-829, September.
    2. Ursa Pantle & Volker Schmidt & Evgeny Spodarev, 2010. "On the Estimation of Integrated Covariance Functions of Stationary Random Fields," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(1), pages 47-66, March.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:118:y:2008:i:2:p:213-231. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.