Estimating the J function without edge correction

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dc.creatorBaddeley, Adrian
dc.creatorKerscher, Martin
dc.creatorSchladitz, Katja
dc.creatorScott, Bryan T.
dc.date1999-10-04
dc.date.accessioned2026-07-07T08:08:54Z
dc.date.available2026-07-07T08:08:54Z
dc.descriptionThe 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 {\em 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 $\hat{J}_W$ of J computed from uncorrected estimates of F and G. The function $J_W(r)$, estimated by $\hat{J}_W$, 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 $J_W(r)(r)\equiv 1$. Computer simulations suggest this test is at least as powerful as tests based on edge corrected estimators of J.
dc.descriptionto appaer in Statistica Neerlandica, LaTeX, 15 pages with 5 figures
dc.identifierhttps://arxiv.org/abs/math/9910011
dc.identifierhttp://arxiv.org/abs/math/9910011
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/131421
dc.subjectStatistics Theory
dc.subjectProbability
dc.subject62M30, 60D05, 65C05, 60G55
dc.titleEstimating the J function without edge correction
dc.typetext

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