Geodesic
Estimation of summary characteristics from replicated spatial point processes
Kybernetika, Tome 47 (2011) no. 6, pp. 880-892 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Summary characteristics play an important role in the analysis of spatial point processes. We discuss various approaches to estimating summary characteristics from replicated observations of a stationary point process. The estimators are compared with respect to their integrated squared error. Simulations for three basic types of point processes help to indicate the best way of pooling the subwindow estimators. The most appropriate way depends on the particular summary characteristic, edge-correction method and also on the type of point process. The methods are demonstrated on a replicated dataset from forestry.
Summary characteristics play an important role in the analysis of spatial point processes. We discuss various approaches to estimating summary characteristics from replicated observations of a stationary point process. The estimators are compared with respect to their integrated squared error. Simulations for three basic types of point processes help to indicate the best way of pooling the subwindow estimators. The most appropriate way depends on the particular summary characteristic, edge-correction method and also on the type of point process. The methods are demonstrated on a replicated dataset from forestry.
Classification : 60G55, 62G05, 62M30
Keywords: $K$-function; nearest-neighbour distance distribution function; non-parametric estimation; point process; replication 
@article{KYB_2011_47_6_a5,
     author = {Pawlas, Zbyn\v{e}k},
     title = {Estimation of summary characteristics from replicated spatial point processes},
     journal = {Kybernetika},
     pages = {880--892},
     year = {2011},
     volume = {47},
     number = {6},
     mrnumber = {2907848},
     zbl = {1250.62042},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2011_47_6_a5/}
}
TY  - JOUR
AU  - Pawlas, Zbyněk
TI  - Estimation of summary characteristics from replicated spatial point processes
JO  - Kybernetika
PY  - 2011
SP  - 880
EP  - 892
VL  - 47
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/KYB_2011_47_6_a5/
LA  - en
ID  - KYB_2011_47_6_a5
ER  - 
%0 Journal Article
%A Pawlas, Zbyněk
%T Estimation of summary characteristics from replicated spatial point processes
%J Kybernetika
%D 2011
%P 880-892
%V 47
%N 6
%U http://geodesic.mathdoc.fr/item/KYB_2011_47_6_a5/
%G en
%F KYB_2011_47_6_a5
Pawlas, Zbyněk. Estimation of summary characteristics from replicated spatial point processes. Kybernetika, Tome 47 (2011) no. 6, pp. 880-892. http://geodesic.mathdoc.fr/item/KYB_2011_47_6_a5/

[1] Baddeley, A. J., Gill, R.: Kaplan-Meier estimators of distance distributions for spatial point processes. Ann. Statist. 25 (1997), 263-292. | DOI | MR | Zbl

[2] Baddeley, A. J., Moyeed, R. A., Howard, C. V., Boyde, A.: Analysis of a three-dimensional point pattern with replication. J. Roy. Statist. Soc. Ser. C 42 (1993), 641-668. | MR | Zbl

[3] Bell, M. L., Grunwald, G. K.: Mixed models for the analysis of replicated spatial point patterns. Biostatistics 5 (2004), 633-648. | DOI | Zbl

[4] Diggle, P. J.: Statistical Analysis of Spatial Point Patterns. 2nd edition. Arnold, London 2003. | MR | Zbl

[5] Diggle, P. J., Lange, N., Beneš, F. M.: Analysis of variance for replicated spatial point patterns in clinical neuroanatomy. J. Amer. Statist. Assoc. 86 (1991), 618-625. | DOI

[6] Diggle, P. J., Mateu, J., Clough, H. E.: A comparison between parametric and non-parametric approaches to the analysis of replicated spatial point patterns. Adv. in Appl. Probab. (SGSA) 32 (2000), 331-343. | DOI | MR | Zbl

[7] Hanisch, K.-H.: Some remarks on estimators of the distribution function of nearest neighbour distance in stationary spatial point patterns. Statistics 15 (1984), 409-412. | MR

[8] Illian, J., Penttinen, A., Stoyan, H., Stoyan, D.: Statistical Analysis and Modeling of Spatial Point Patterns. John Wiley & Sons, Chichester 2008. | MR

[9] Philimonenko, A. A., Janáček, J., Hozák, P.: Statistical evaluation of colocalization patterns in immunogold labeling experiments. J. Struct. Biol. 132 (2000), 201-210. | DOI

[10] R Development Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna 2010. URL: http://www.R-project.org

[11] Stoyan, D.: On estimators of the nearest neighbour distance distribution function for stationary point processes. Metrika 64 (2006), 139-150. | DOI | MR | Zbl

[12] Wager, C. G., Coull, B. A., Lange, N.: Modelling spatial intensity for replicated inhomogeneous point patterns in brain imaging. J. R. Statist. Soc. B 66 (2004), 429-446. | DOI | MR | Zbl