IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v16y2014i2d10.1007_s11009-013-9358-3.html
   My bibliography  Save this article

Estimating Second-Order Characteristics of Inhomogeneous Spatio-Temporal Point Processes

Author

Listed:
  • Edith Gabriel

    (Avignon University)

Abstract

Non-parametric estimates of the K-function and the pair correlation function play a fundamental role for exploratory and explanatory analysis of spatial and spatio-temporal point patterns. These estimates usually require information from outside of the study region, resulting to the so-called edge effects which have to be corrected. They also depend on first-order characteristics, which have to be estimated in practice. In this paper, we extend classical edge correction methods to the spatio-temporal setting and compare the performance of the related estimators for stationary/non-stationary and/or isotropic/anisotropic point patterns. Further, we explore the influence of the estimated intensity function on these estimators.

Suggested Citation

  • Edith Gabriel, 2014. "Estimating Second-Order Characteristics of Inhomogeneous Spatio-Temporal Point Processes," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 411-431, June.
    • Handle: RePEc:spr:metcap:v:16:y:2014:i:2:d:10.1007_s11009-013-9358-3
    DOI: 10.1007/s11009-013-9358-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-013-9358-3
    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/s11009-013-9358-3?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. Yongtao Guan & Michael Sherman & James A. Calvin, 2006. "Assessing Isotropy for Spatial Point Processes," Biometrics, The International Biometric Society, vol. 62(1), pages 119-125, March.
    2. Mark Berman & T. Rolf Turner, 1992. "Approximating Point Process Likelihoods with Glim," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(1), pages 31-38, March.
    3. P. J. Diggle & V. Gómez-Rubio & P. E. Brown & A. G. Chetwynd & S. Gooding, 2007. "Second-Order Analysis of Inhomogeneous Spatial Point Processes Using Case–Control Data," Biometrics, The International Biometric Society, vol. 63(2), pages 550-557, June.
    4. 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.
    5. Cronie, Ottmar & Särkkä, Aila, 2011. "Some edge correction methods for marked spatio-temporal point process models," Computational Statistics & Data Analysis, Elsevier, vol. 55(7), pages 2209-2220, July.
    6. Gabriel, Edith & Rowlingson, Barry S. & Diggle, Peter J., 2013. "stpp: An R Package for Plotting, Simulating and Analyzing Spatio-Temporal Point Patterns," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 53(i02).
    7. Arbia, G. & Espa, G. & Giuliani, D. & Mazzitelli, A., 2012. "Clusters of firms in an inhomogeneous space: The high-tech industries in Milan," Economic Modelling, Elsevier, vol. 29(1), pages 3-11.
    8. Denis Allard & Anders Brix & Joël Chadoeuf, 2001. "Testing Local Independence between Two Point Processes," Biometrics, The International Biometric Society, vol. 57(2), pages 508-517, June.
    9. 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.
    10. Jesper Møller & Mohammad Ghorbani, 2012. "Aspects of second-order analysis of structured inhomogeneous spatio-temporal point processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(4), pages 472-491, November.
    11. Peter Diggle, 1985. "A Kernel Method for Smoothing Point Process Data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 34(2), pages 138-147, 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. Jiří Dvořák & Michaela Prokešová, 2016. "Parameter Estimation for Inhomogeneous Space-Time Shot-Noise Cox Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(4), pages 939-961, December.
    2. Eckardt, Matthias & González, Jonatan A. & Mateu, Jorge, 2021. "Graphical modelling and partial characteristics for multitype and multivariate-marked spatio-temporal point processes," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    3. Mohammad Ghorbani & Ottmar Cronie & Jorge Mateu & Jun Yu, 2021. "Functional marked point processes: a natural structure to unify spatio-temporal frameworks and to analyse dependent functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 529-568, September.

    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. Ghorbani, Mohammad & Vafaei, Nafiseh & Dvořák, Jiří & Myllymäki, Mari, 2021. "Testing the first-order separability hypothesis for spatio-temporal point patterns," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    2. 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.
    3. 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.
    4. 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.
    5. Nicoletta D’Angelo & Giada Adelfio & Jorge Mateu, 2023. "Local inhomogeneous second-order characteristics for spatio-temporal point processes occurring on linear networks," Statistical Papers, Springer, vol. 64(3), pages 779-805, June.
    6. C. Comas & F. J. Rodriguez-Cortes & J. Mateu, 2015. "Second-order analysis of anisotropic spatiotemporal point process data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 69(1), pages 49-66, February.
    7. Nicoletta D’Angelo & Giada Adelfio, 2024. "Minimum contrast for the first-order intensity estimation of spatial and spatio-temporal point processes," Statistical Papers, Springer, vol. 65(6), pages 3651-3679, August.
    8. Eckardt, Matthias & González, Jonatan A. & Mateu, Jorge, 2021. "Graphical modelling and partial characteristics for multitype and multivariate-marked spatio-temporal point processes," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    9. Michaela Prokešová & Jiří Dvořák, 2014. "Statistics for Inhomogeneous Space-Time Shot-Noise Cox Processes," Methodology and Computing in Applied Probability, Springer, vol. 16(2), pages 433-449, June.
    10. 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.
    11. 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).
    12. Jesper Møller & Heidi S. Christensen & Francisco Cuevas-Pacheco & Andreas D. Christoffersen, 2021. "Structured Space-Sphere Point Processes and K-Functions," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 569-591, June.
    13. Zhang, Tonglin & Mateu, Jorge, 2019. "Substationarity for spatial point processes," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 22-36.
    14. 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.
    15. 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.
    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. Eric Marcon & Florence Puech, 2009. "Generalizing Ripley's K function to inhomogeneous populations," Working Papers halshs-00372631, HAL.
    18. Mohammad Ghorbani & Ottmar Cronie & Jorge Mateu & Jun Yu, 2021. "Functional marked point processes: a natural structure to unify spatio-temporal frameworks and to analyse dependent functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(3), pages 529-568, September.
    19. P. J. Diggle & V. Gómez-Rubio & P. E. Brown & A. G. Chetwynd & S. Gooding, 2007. "Second-Order Analysis of Inhomogeneous Spatial Point Processes Using Case–Control Data," Biometrics, The International Biometric Society, vol. 63(2), pages 550-557, June.
    20. Jeffrey Daniel & Julie Horrocks & Gary J. Umphrey, 2020. "Efficient Modelling of Presence-Only Species Data via Local Background Sampling," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 25(1), pages 90-111, 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:spr:metcap:v:16:y:2014:i:2:d:10.1007_s11009-013-9358-3. 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.