Estimating the J function without edge correction

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 J W ( r ), estimated by ? W , possesses similar properties to the J function, for example J W ( 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 J W ( r ) ≡ 1. Computer simulations suggest this test is at least as powerful as tests based on edge corrected estimators of J .