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Estimating the J function without edge correction
Author(s) -
Baddeley A. J.,
Kerscher M.,
Schladitz K.,
Scott B. T.
Publication year - 2000
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/1467-9574.00143
Subject(s) - mathematics , estimator , monte carlo method , point process , independent and identically distributed random variables , poisson distribution , function (biology) , empirical distribution function , randomness , bounded function , statistics , combinatorics , random variable , mathematical analysis , evolutionary biology , biology
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 .