TESTING RANDOMNESS OF SPATIAL POINT PATTERNS WITH THE RIPLEY STATISTIC
TESTING RANDOMNESS OF SPATIAL POINT PATTERNS WITH THE RIPLEY STATISTIC
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DOI：
10.1051/ps/2012027
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发表时间：
2013-01-01
影响因子：
0.4
通讯作者：
Marcon, Eric
中科院分区：
文献类型：
--
作者：
Lang, Gabriel;Marcon, Eric
聚集模式通常在位置数据集中被视觉地检测到。这些集群可能是有趣的动力学的结果，也可能是纯粹随机性的影响。我们建立了一个渐近高斯检验的随机性对应的齐次泊松点过程的假设。我们首先计算齐次泊松点过程模型下Ripley K-统计量的精确一阶矩和二阶矩。然后，我们证明了这种统计量的一个向量的渐近正态性为不同的尺度，并计算其协方差矩阵。从这些结果中，我们得到一个检验统计量，卡方分布。通过蒙特-卡罗研究，我们检查了测试是数值上易于处理的，即使是大的数据集，也正确的，当只有一百个点观察。
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.