# zbMATH — the first resource for mathematics

Quasi-plus sampling edge correction for spatial point patterns. (English) Zbl 1452.62705
Summary: A widely applicable edge correction method for estimating summary statistics of a spatial point pattern is proposed. We reconstruct point patterns in a larger region containing the sampling window by matching sampled and simulated $$k$$th nearest neighbour distance distributions of the given pattern and then apply plus sampling. Simulation studies show that this approach, called quasi-plus sampling, gives estimates with smaller root mean squared errors than estimates obtained by using other popular edge corrections. We apply the proposed approach to real data and yield an estimate of a summary statistic that is more plausible than that obtained by a popular edge correction.

##### MSC:
 62M30 Inference from spatial processes 62-08 Computational methods for problems pertaining to statistics
Full Text:
##### References:
 [1] Baddeley, A., Sampling and censoring, (), 37-78 [2] Baddeley, A.; Gill, R.D., Kaplan – meier estimators of distance distributions for spatial point processes, Annals of statistics, 25, 263-292, (1997) · Zbl 0870.62028 [3] Chiu, S.N.; Stoyan, D., Estimators of distance distributions for spatial patterns, Statistica neerlandica, 52, 239-246, (1998) · Zbl 0954.62110 [4] Doguwa, S.I.; Upton, G.J.G., On the estimation of the nearest neighbour distribution, $$G(t)$$, for point processes, Biometrical journal, 32, 863-876, (1990) [5] Floresroux, E.M.; Stein, M.L., A new method of edge correction for estimating the nearest neighbour distribution, Journal of statistical planning and inference, 50, 353-371, (1996) · Zbl 0848.62050 [6] Hanisch, K.-H., Some remarks on estimators of the distribution function of nearest neighbour distance in stationary spatial point processes, Mathematische operationsforschung und statistik series statistics, 15, 409-412, (1984) · Zbl 0553.62076 [7] Illian, J.; Penttinen, A.; Stoyan, H.; Stoyan, D., Statistical analysis and modelling of spatial point patterns, (2008), John Wiley Chichester · Zbl 1197.62135 [8] Reed, M.G.; Howard, C.V., Edge-corrected estimators of the nearest-neighbour distance distribution function for three-dimensional point patterns, Journal of microscopy, 186, 177-184, (1997) [9] Stoyan, D., On estimators of the nearest neighbour distance distribution function for stationary point processes, Metrika, 64, 139-150, (2006) · Zbl 1100.62082 [10] Stoyan, D.; Kendall, W.S.; Mecke, J., Stochastic geometry and its applications, (1995), John Wiley Chichester · Zbl 0838.60002 [11] Stoyan, D.; Stoyan, H., Improving ratio estimators of second order point process characteristics, Scandinavian journal of statistics, 27, 641-656, (2000) · Zbl 0963.62089 [12] Tscheschel, A.; Stoyan, D., Reconstruction of point patterns, Computational statistics and data analysis, 51, 859-871, (2006) · Zbl 1157.62453 [13] van Lieshout, M.N.M.; Baddeley, A.J., Extrapolating and interpolating spatial patterns, (), 61-86
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.