TY  - JOUR
AU  - Lang, G.
AU  - Marcon, E.
PY  - 2013//
TI  - Testing randomness of spatial point patterns with the Ripley statistic
T2  - ESAIM PS
JO  - ESAIM: Probability and Statistics
SP  - 767
EP  - 788
VL  - 17
KW  - Central limit theorem
KW  - goodness-of-fit test
KW  - Höffding decomposition
KW  - null
KW  - point pattern
KW  - Poisson process
N2  - Aggregation patterns are often visually detected in sets of location data. These clusters may be the result of interesting dynamics or the effect of pure randomness. We build an asymptotically Gaussian test for the hypothesis of randomness corresponding to a homogeneous Poisson point process. We first compute the exact first and second moment of the Ripley K-statistic under the homogeneous Poisson point process model. Then we prove the asymptotic normality of a vector of such statistics for different scales and compute its covariance matrix. From these results, we derive a test statistic that is chi-square distributed. By a Monte-Carlo study, we check that the test is numerically tractable even for large data sets and also correct when only a hundred of points are observed
UR  - http://dx.doi.org/10.1051/ps/2012027
N1  - exported from refbase (http://php.ecofog.gf/refbase/show.php?record=518), last updated on Thu, 12 Dec 2013 11:44:54 -0300
ID  - Lang+Marcon2013
ER  -