Estimating the J function without edge correction

Van Lieshout and Baddeley introduced the function J = (1 \Gamma G)=(1 \Gamma F ) as a measure of interaction in a spatial point process. Here G is the nearest-neighbour distance distribution function and F the empty space function. As is the case for all distance methods, estimating J is hampered by edge effects. In this paper we consider what happens if these edge effects are simply ignored and an estimate b JW is computed from the uncorrected, empirical distributions of distances observed in a window W . We find the function JW (r), estimated by b JW , 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) j 1. Computer simulations suggest this test is at least as powerful as tests based on edg..