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Detecting dependence between marks and locations of marked point processes. (English) Zbl 1061.62151
Summary: We introduce two characteristics for stationary and isotropic marked point processes, \(E(h)\) and \(V(h)\), and describe their use in investigating mark-point interactions. These quantities are functions of the interpoint distance \(h\) and denote the conditional expectation and the conditional variance of a mark, respectively, given that there is a further point of the process a distance \(h\) away. We present tests based on \(E\) and \(V\) for the hypothesis that the values of the marks can be modelled by a random field which is independent of the unmarked point process. We apply the methods to two data sets in forestry.

MSC:
62M40 Random fields; image analysis
86A32 Geostatistics
62M07 Non-Markovian processes: hypothesis testing
62M30 Inference from spatial processes
Software:
GSLIB; R; spatial
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