Estimating the J function without edge correction

A. J. Baddeley, M. Kerscher, K. Schladitz and B. T. Scott

Statistica Neerlandica, 2000, vol. 54, issue 3, 315-328

Abstract: The interaction between points in a spatial point process can be measured by its empty space function F, its nearest‐neighbour distance distribution function G, and by combinations such as the J function J = (1 −G)/(1 −F). The estimation of these functions is hampered by edge effects: the uncorrected, empirical distributions of distances observed in a bounded sampling window W give severely biased estimates of F and G. However, in this paper we show that the corresponding uncorrected estimator of the function J = (1 −G)/(1 −F) is approximately unbiased for the Poisson case, and is useful as a summary statistic. Specifically, consider the estimate ?W of J computed from uncorrected estimates of F and G. The function JW(r), estimated by ?W, possesses similar properties to the J function, for example JW(r) is identically 1 for Poisson processes. This enables direct interpretation of uncorrected estimates of J, something not possible with uncorrected estimates of either F, G or K. We propose a Monte Carlo test for complete spatial randomness based on testing whether JW(r) ≡ 1. Computer simulations suggest this test is at least as powerful as tests based on edge corrected estimators of J.

Date: 2000
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