ESTIMATION VARIANCES FOR ESTIMATORS OF PRODUCT DENSITIES AND PAIR CORRELATION FUNCTIONS OF

PLANAR POINT PROCESSES

D. STOYAN^{1}, U. BERTRAM^{2} AND H. WENDROCK^{2}

1Fachbereich Mathematik, Bergakademie Freiberg, 09596 Freiberg, Germany 2Institut für Strukturforschung und Festkörperphysik Dresden, 01171 Dresden, Germany

(Received November 22, 1991; revised July 13, 1992)

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.

Key words and phrases: Approximation, estimation variance, pair correlation function, Poisson process, product density, simulation.