IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v16y2014i2d10.1007_s11009-013-9335-x.html
   My bibliography  Save this article

On Random Marked Sets with a Smaller Integer Dimension

Author

Listed:
  • Jakub Staněk

    (Charles University in Prague)

  • Ondřej Šedivý

    (Charles University in Prague)

  • Viktor Beneš

    (Charles University in Prague)

Abstract

The paper deals with random marked sets in ${\mathbb R}^d$ which have integer dimension smaller than d. Statistical analysis is developed which involves the random-field model test and estimation of first and second-order characteristics. Special models are presented based on tessellations and solutions of stochastic differential equations (SDE). The simulation of these sets makes use of marking by means of Gaussian random fields. A space-time nature of the model based on SDE is taken into account. Numerical results of the estimation and testing are discussed. Real data analysis from the materials research investigating a grain microstructure with disorientations of faces as marks is presented.

Suggested Citation

  • Jakub Staněk & Ondřej Šedivý & Viktor Beneš, 2014. "On Random Marked Sets with a Smaller Integer Dimension," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 397-410, June.
    • Handle: RePEc:spr:metcap:v:16:y:2014:i:2:d:10.1007_s11009-013-9335-x
    DOI: 10.1007/s11009-013-9335-x
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-013-9335-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-013-9335-x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. A. J. Baddeley & J. Møller & R. Waagepetersen, 2000. "Non‐ and semi‐parametric estimation of interaction in inhomogeneous point patterns," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 54(3), pages 329-350, November.
    2. Pawlas, Zbynek, 2009. "Empirical distributions in marked point processes," Stochastic Processes and their Applications, Elsevier, vol. 119(12), pages 4194-4209, December.
    3. Grabarnik, Pavel & Myllymäki, Mari & Stoyan, Dietrich, 2011. "Correct testing of mark independence for marked point patterns," Ecological Modelling, Elsevier, vol. 222(23), pages 3888-3894.
    4. Martin Schlather & Paulo J. Ribeiro & Peter J. Diggle, 2004. "Detecting dependence between marks and locations of marked point processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 79-93, February.
    Full references (including those not matched with items on IDEAS)

    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. Lothar Heinrich & Stella Klein & Martin Moser, 2014. "Empirical Mark Covariance and Product Density Function of Stationary Marked Point Processes—A Survey on Asymptotic Results," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 283-293, June.
    2. Florent Bonneu & Christine Thomas-Agnan, 2015. "Measuring and Testing Spatial Mass Concentration with Micro-geographic Data," Spatial Economic Analysis, Taylor & Francis Journals, vol. 10(3), pages 289-316, September.
    3. O. Cronie & M. N. M. Van Lieshout, 2015. "A J -function for Inhomogeneous Spatio-temporal Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(2), pages 562-579, June.
    4. Elvan Ceyhan, 2009. "Class‐specific tests of spatial segregation based on nearest neighbor contingency tables," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 63(2), pages 149-182, May.
    5. Jesper Møller & Håkon Toftaker, 2014. "Geometric Anisotropic Spatial Point Pattern Analysis and Cox Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 414-435, June.
    6. Jiří Dvořák & Tomáš Mrkvička & Jorge Mateu & Jonatan A. González, 2022. "Nonparametric Testing of the Dependence Structure Among Points–Marks–Covariates in Spatial Point Patterns," International Statistical Review, International Statistical Institute, vol. 90(3), pages 592-621, December.
    7. Giuseppe Espa & Giuseppe Arbia & Diego Giuliani, 2013. "Conditional versus unconditional industrial agglomeration: disentangling spatial dependence and spatial heterogeneity in the analysis of ICT firms’ distribution in Milan," Journal of Geographical Systems, Springer, vol. 15(1), pages 31-50, January.
    8. Edith Gabriel & Peter J. Diggle, 2009. "Second‐order analysis of inhomogeneous spatio‐temporal point process data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 63(1), pages 43-51, February.
    9. Arbia, Giuseppe & Espa, Giuseppe & Giuliani, Diego & Dickson, Maria Michela, 2014. "Spatio-temporal clustering in the pharmaceutical and medical device manufacturing industry: A geographical micro-level analysis," Regional Science and Urban Economics, Elsevier, vol. 49(C), pages 298-304.
    10. Kateřina Koňasová & Jiří Dvořák, 2021. "Stochastic Reconstruction for Inhomogeneous Point Patterns," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 527-547, June.
    11. Redenbach, Claudia & Särkkä, Aila, 2013. "Parameter estimation for growth interaction processes using spatio-temporal information," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 672-683.
    12. Saltré, F. & Chuine, I. & Brewer, S. & Gaucherel, C., 2009. "A phenomenological model without dispersal kernel to model species migration," Ecological Modelling, Elsevier, vol. 220(24), pages 3546-3554.
    13. Eric Marcon & Florence Puech, 2012. "A typology of distance-based measures of spatial concentration," Working Papers halshs-00679993, HAL.
    14. Giuseppe Arbia & Patrizia Cella & Giuseppe Espa & Diego Giuliani, 2015. "A micro spatial analysis of firm demography: the case of food stores in the area of Trento (Italy)," Empirical Economics, Springer, vol. 48(3), pages 923-937, May.
    15. D'Angelo, Nicoletta & Adelfio, Giada & Mateu, Jorge, 2023. "Locally weighted minimum contrast estimation for spatio-temporal log-Gaussian Cox processes," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    16. Ondřej Šedivý & Antti Penttinen, 2014. "Intensity estimation for inhomogeneous Gibbs point process with covariates-dependent chemical activity," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 68(3), pages 225-249, August.
    17. Marcon, Eric & Puech, Florence, 2017. "A typology of distance-based measures of spatial concentration," Regional Science and Urban Economics, Elsevier, vol. 62(C), pages 56-67.
    18. Amanda S. Hering & Sean Bair, 2014. "Characterizing spatial and chronological target selection of serial offenders," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(1), pages 123-140, January.
    19. Ho, Lai Ping & Stoyan, D., 2008. "Modelling marked point patterns by intensity-marked Cox processes," Statistics & Probability Letters, Elsevier, vol. 78(10), pages 1194-1199, August.
    20. Tilman M. Davies & Martin L. Hazelton, 2013. "Assessing minimum contrast parameter estimation for spatial and spatiotemporal log‐Gaussian Cox processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 67(4), pages 355-389, November.

    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:spr:metcap:v:16:y:2014:i:2:d:10.1007_s11009-013-9335-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.