Moment estimation methods for stationary spatial Cox processes - A comparison

Jiří Dvořák; Michaela Prokešová

Kybernetika (2012)

  • Volume: 48, Issue: 5, page 1007-1026
  • ISSN: 0023-5954

Abstract

top
In the present paper we consider the problem of fitting parametric spatial Cox point process models. We concentrate on the moment estimation methods based on the second order characteristics of the point process in question. These methods represent a simulation-free faster-to-compute alternative to the computationally intense maximum likelihood estimation. We give an overview of the available methods, discuss their properties and applicability. Further we present results of a simulation study in which performance of these estimating methods was compared for planar point processes with different types and strength of clustering and inter-point interactions.

How to cite

top

Dvořák, Jiří, and Prokešová, Michaela. "Moment estimation methods for stationary spatial Cox processes - A comparison." Kybernetika 48.5 (2012): 1007-1026. <http://eudml.org/doc/251433>.

@article{Dvořák2012,
abstract = {In the present paper we consider the problem of fitting parametric spatial Cox point process models. We concentrate on the moment estimation methods based on the second order characteristics of the point process in question. These methods represent a simulation-free faster-to-compute alternative to the computationally intense maximum likelihood estimation. We give an overview of the available methods, discuss their properties and applicability. Further we present results of a simulation study in which performance of these estimating methods was compared for planar point processes with different types and strength of clustering and inter-point interactions.},
author = {Dvořák, Jiří, Prokešová, Michaela},
journal = {Kybernetika},
keywords = {moment estimation methods; spatial Cox point process; parametric inference; moment estimation methods; spatial Cox point process; parametric inference},
language = {eng},
number = {5},
pages = {1007-1026},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Moment estimation methods for stationary spatial Cox processes - A comparison},
url = {http://eudml.org/doc/251433},
volume = {48},
year = {2012},
}

TY - JOUR
AU - Dvořák, Jiří
AU - Prokešová, Michaela
TI - Moment estimation methods for stationary spatial Cox processes - A comparison
JO - Kybernetika
PY - 2012
PB - Institute of Information Theory and Automation AS CR
VL - 48
IS - 5
SP - 1007
EP - 1026
AB - In the present paper we consider the problem of fitting parametric spatial Cox point process models. We concentrate on the moment estimation methods based on the second order characteristics of the point process in question. These methods represent a simulation-free faster-to-compute alternative to the computationally intense maximum likelihood estimation. We give an overview of the available methods, discuss their properties and applicability. Further we present results of a simulation study in which performance of these estimating methods was compared for planar point processes with different types and strength of clustering and inter-point interactions.
LA - eng
KW - moment estimation methods; spatial Cox point process; parametric inference; moment estimation methods; spatial Cox point process; parametric inference
UR - http://eudml.org/doc/251433
ER -

References

top
  1. Baddeley, A. J., Turner, R., 10.1111/1467-842X.00128, Aust. N. Z. J. Statist. 42 (2000), 283-322. MR1794056DOI10.1111/1467-842X.00128
  2. Baddeley, A. J., Turner, R., Spatstat: an R package for analyzing spatial point patterns., J. Statist. Softw. 12 (2005), 1-42. 
  3. Brix, A., 10.1239/aap/1029955251, Adv. in Appl. Probab. 31 (1999), 929-953. Zbl0957.60055MR1747450DOI10.1239/aap/1029955251
  4. Cox, D. R., Some statistical models related with series of events., J. Roy. Statist. Soc. Ser. B 17 (1955), 129-164. MR0092301
  5. Daley, D. J., Vere-Jones, D., An Introduction to the Theory of Point Processes. Volume 1: Elementary Theory and Methods., Second edition. Springer Verlag, New York 2003. MR1950431
  6. Daley, D. J., Vere-Jones, D., An Introduction to the Theory of Point Processes. Volume 2: General Theory and Structure., Second edition. Springer Verlag, New York 2008. MR2371524
  7. Diggle, P. J., Statistical Analysis of Spatial Point Patterns., Academic Press, London 1983. Zbl1021.62076MR0743593
  8. Diggle, P. J., Statistical Analysis of Spatial Point Patterns., Second edition. Oxford University Press, New York 2003. Zbl1021.62076MR0743593
  9. Dvořák, J., Prokešová, M., Moment estimation methods for stationary spatial Cox processes - a simulation study., Preprint (2011), . 
  10. Guan, Y., 10.1198/016214506000000500, J. Amer. Statist. Assoc. 101 (2006), 1502-1512. Zbl1171.62348MR2279475DOI10.1198/016214506000000500
  11. Guan, Y., Sherman, M., 10.1111/j.1467-9868.2007.00575.x, J. Roy. Statist. Soc. Ser. B 69 (2007), 31-49. MR2301498DOI10.1111/j.1467-9868.2007.00575.x
  12. Heinrich, L., Minimum contrast estimates for parameters of spatial ergodic point processes., In: Trans. 11th Prague Conference on Random Processes, Information Theory and Statistical Decision Functions. Academic Publishing House, Prague 1992. 
  13. Hellmund, G., Prokešová, M., Jensen, E. B. Vedel, 10.1239/aap/1222868178, Adv. in Appl. Probab. 40 (2008), 603-629. MR2454025DOI10.1239/aap/1222868178
  14. Illian, J., Penttinen, A., Stoyan, H., Stoyan, D., Statistical Analysis and Modelling of Spatial Point Patterns., John Wiley and Sons, Chichester 2008. Zbl1197.62135MR2384630
  15. Jensen, A. T., Statistical Inference for Doubly Stochastic Poisson Processes., Ph.D. Thesis, Department of Applied Mathematics and Statistics, University of Copenhagen 2005. 
  16. Lindsay, B. G., 10.1090/conm/080/999014, Contemp. Math. 80 (1988), 221-239. Zbl0672.62069MR0999014DOI10.1090/conm/080/999014
  17. Matérn, B., Doubly stochastic Poisson processes in the plane., In: Statistical Ecology. Volume 1. Pennsylvania State University Press, University Park 1971. 
  18. Møller, J., Syversveen, A. R., Waagepetersen, R. P., 10.1111/1467-9469.00115, Scand. J. Statist. 25 (1998), 451-482. MR1650019DOI10.1111/1467-9469.00115
  19. Møller, J., 10.1239/aap/1059486821, Adv. in Appl. Probab. (SGSA) 35 (2003), 614-640. MR1990607DOI10.1239/aap/1059486821
  20. Møller, J., Waagepetersen, R. P., Statistical Inference and Simulation for Spatial Point Processes., Chapman and Hall/CRC, Florida 2003. 
  21. Møller, J., Waagepetersen, R. P., Modern statistics for spatial point processes., Scand. J. Statist. 34 (2007), 643-684. MR2392447
  22. Prokešová, M., Jensen, E. B. Vedel, Asymptotic Palm likelihood theory for stationary spatial point processes., Accepted to Ann. Inst. Statist. Math. (2012). 
  23. Tanaka, U., Ogata, Y., Stoyan, D., Parameter estimation and model selection for Neyman-Scott point processes., Biometrical J. 49 (2007), 1-15. MR2414637

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.