Abstract
Approximations of the estimation variances of kernel estimators of the pair correlation function and the product density of a planar Poisson process are given. Furthermore, a heuristic approximation of the estimation variance of an estimator of the pair correlation function of a “general” planar point process is suggested. All formulae have been tested by simulation experiments.
This is a preview of subscription content, log in via an institution to check access.
We’re sorry, something doesn't seem to be working properly.
Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.
References
Doguwa, S. I. (1990). On edge-corrected kernel-based pair-correlation function estimators for point processes,Biometrical J.,32, 95–106.
Fiksel, T. (1988). Edge-corrected density estimators for point processes,Statistics,19, 67–75.
Ohser, J. (1991). On estimation of pair correlation functions,Geometrical Problems of Image Processing (eds. U. Eckhardt, A. Hübler, W. Nagel, and G. Werner), 147–152, Akademie Verlag, Berlin.
Penttinen, A. K. and Stoyan, D. (1989). Statistical analysis for a class of line segment processes,Scand. J. Statist.,16, 152–168.
Ripley, B. D. (1977). Modelling spatial patterns (with discussion),J. Roy. Statist. Soc. Ser. B,39, 172–212.
Ripley, B. D. (1981).Spatial Statistics, Wiley, New York.
Ripley, B. D. (1988).Statistical Inference for Spatial Processes, Cambridge University Press, Cambridge.
Stoyan, D., Kendall, W. S. and J. Mecke (1987).Stochastic Geometry and Its Applications, Wiley, Chichester.
Author information
Authors and Affiliations
About this article
Cite this article
Stoyan, D., Bertram, U. & Wendrock, H. Estimation variances for estimators of product densities and pair correlation functions of planar point processes. Ann Inst Stat Math 45, 211–221 (1993). https://doi.org/10.1007/BF00775808
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00775808