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On Estimators of the Nearest Neighbour Distance Distribution Function for Stationary Point Processes
Authors:Email author" target="_blank">Dietrich?StoyanEmail author
Institution:(1) Institut für Stochastik, TU Bergakademie Freiberg, Freiberg, 09596, Germany
Abstract:There are three approaches for the estimation of the distribution function D(r) of distance to the nearest neighbour of a stationary point process: the border method, the Hanisch method and the Kaplan-Meier approach. The corresponding estimators and some modifications are compared with respect to bias and mean squared error (mse). Simulations for Poisson, cluster and hard-core processes show that the classical border estimator has good properties; still better is the Hanisch estimator. Typically, mse depends on r, having small values for small and large r and a maximum in between. The mse is not reduced if the exact intensity λ (if known) or intensity estimators from larger windows are built in the estimators of D(r); in contrast, the intensity estimator should have the same precision as that of λ D(r). In the case of replicated estimation from more than one window the best way of pooling the subwindow estimates is averaging by weights which are proportional to squared point numbers.
Keywords:Stationary point process  Nearest neighbour distance distribution  Hanisch estimator  Mean squared deviation  Replication
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