# zbMATH — the first resource for mathematics

A new method of edge correction for estimating the nearest neighbor distribution. (English) Zbl 0848.62050
Summary: Analysis of data in the form of a set of points irregularly distributed within a region of space usually involves the study of some property of the distribution of inter-event distances. One such function is $$G$$, the distribution of the distance from an event to its nearest neighbor. In practice, point processes are commonly observed through a bounded window, thus making edge effects an important component in the estimation of $$G$$. Several estimators have been proposed, all dealing with the edge effect problem in different ways. This paper proposes a new alternative for estimating the nearest neighbor distribution and compares it to other estimators. The result is an estimator with relatively small mean squared error for a wide variety of stationary processes.

##### MSC:
 62M30 Inference from spatial processes 62H11 Directional data; spatial statistics
spatial
Full Text:
##### References:
 [1] Baddeley, A.J.; Gill, R.D., Kaplan-meier estimators of interpoint distance distributions for spatial point processes, () · Zbl 0870.62028 [2] Baddeley, A.J.; Moyeed, R.A.; Howard, C.V.; Reid, S.; Boyde, E., Analysis of a three-dimensional point pattern with replication, Appl. statist., 42, 641-668, (1993) · Zbl 0825.62476 [3] Bartlett, M.S., The statistical analysis of spatial pattern, Adv. appl. probab., 6, 336-358, (1974) · Zbl 0311.60035 [4] Daley, D.J.; Vere-Jones, D., An introduction to the theory of point processes, (1988), Springer New York · Zbl 0657.60069 [5] Diggle, P.J., On parameter estimation and goodness-of-fit testing for spatial point patterns, Biometrics, 35, 87-101, (1979) · Zbl 0418.62075 [6] Diggle, P.J., Statistical analysis of spatial point patterns, (1983), Academic Press London · Zbl 0559.62088 [7] Doguwa, S.I.; Upton, G.J.G., On the estimation of the nearest neighbour distribution, G(t), for point processes, Bio. J., 32, 863-876, (1990) [8] Donnelly, K., Simulations to determine the variance and edge effect of total nearest neighbour distance, (), 91-95 [9] Hanisch, K.-H., Some remarks on estimators of the distribution function of nearest neighbour distance is stationary spatial point processes, Math. oper. statist. ser. statist., 15, 409-412, (1984) · Zbl 0553.62076 [10] Neyman, J.; Scott, E.L., Statistical approach to problems of cosmology, J. roy. statist. soc., B 20, 1-43, (1958) · Zbl 0085.42906 [11] Ripley, B.D., Modelling spatial pattern, J. roy. statist. soc., B 39, 172-212, (1977) · Zbl 0369.60061 [12] Ripley, B.D., Statistical inference for spatial processes, (1988), Cambridge Univ. Press Cambridge · Zbl 0716.62100 [13] Stein, M.L., Asymptotically optimal estimation for the reduced second moment measure of point processes, Biometrika, 80, 443-449, (1993) · Zbl 0779.62092 [14] Stoyan, D.; Kendall, W.S.; Mecke, J., Stochastic geometry and its applications, (1987), Wiley New York
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.