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Testing randomness of spatial point patterns with the Ripley statistic

Gabriel LangEric Marcon — 2013

ESAIM: Probability and Statistics

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 -statistic under the homogeneous Poisson point process model. Then we prove the asymptotic normality of a vector of such statistics for different...

Dependent Lindeberg central limit theorem and some applications

Jean-Marc BardetPaul DoukhanGabriel LangNicolas Ragache — 2008

ESAIM: Probability and Statistics

In this paper, a very useful lemma (in two versions) is proved: it simplifies notably the essential step to establish a Lindeberg central limit theorem for dependent processes. Then, applying this lemma to weakly dependent processes introduced in Doukhan and Louhichi (1999), a new central limit theorem is obtained for sample mean or kernel density estimator. Moreover, by using the subsampling, extensions under weaker assumptions of these central limit theorems are provided. All the usual causal...

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