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$K$-function; nearest-neighbour distance distribution function; non-parametric estimation; point process; replication
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.
[1] Baddeley, A. J., Gill, R.: Kaplan-Meier estimators of distance distributions for spatial point processes. Ann. Statist. 25 (1997), 263-292. DOI 10.1214/aos/1034276629 | MR 1429925 | Zbl 0870.62028
[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 1234146 | Zbl 0825.62476
[3] Bell, M. L., Grunwald, G. K.: Mixed models for the analysis of replicated spatial point patterns. Biostatistics 5 (2004), 633-648. DOI 10.1093/biostatistics/kxh014 | Zbl 1069.62055
[4] Diggle, P. J.: Statistical Analysis of Spatial Point Patterns. 2nd edition. Arnold, London 2003. MR 0743593 | Zbl 1021.62076
[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 10.1080/01621459.1991.10475087
[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 10.1239/aap/1013540166 | MR 1778567 | Zbl 1052.60009
[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 0756346
[8] Illian, J., Penttinen, A., Stoyan, H., Stoyan, D.: Statistical Analysis and Modeling of Spatial Point Patterns. John Wiley & Sons, Chichester 2008. MR 2384630
[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 10.1006/jsbi.2000.4326
[10] R Development Core Team: R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna 2010. URL:
[11] Stoyan, D.: On estimators of the nearest neighbour distance distribution function for stationary point processes. Metrika 64 (2006), 139-150. DOI 10.1007/s00184-006-0040-4 | MR 2259218 | Zbl 1100.62082
[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 10.1046/j.1369-7412.2003.05285.x | MR 2062386 | Zbl 1062.62221
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