TY - JOUR

T1 - Estimating the J function without edge correction

AU - Baddeley, Adrian

AU - Kerscher, M.

AU - Scladitz, K.

AU - Scott, B. T.

PY - 2000

Y1 - 2000

N2 - 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 (J) over cap (W) of J computed from uncorrected estimates of F and G. The function J(W)(r), estimated by (J) over cap (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 Carte 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.

AB - 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 (J) over cap (W) of J computed from uncorrected estimates of F and G. The function J(W)(r), estimated by (J) over cap (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 Carte 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.

U2 - 10.1111/1467-9574.00143

DO - 10.1111/1467-9574.00143

M3 - Article

VL - 54

SP - 315

EP - 328

JO - Statistica Neerlandica (Journal of the Netherlands Society for Statistics and Operations Research)

JF - Statistica Neerlandica (Journal of the Netherlands Society for Statistics and Operations Research)

SN - 0039-0402

IS - 3

ER -