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Estimation of summary characteristics from replicated spatial point processes. (English) Zbl 1250.62042
The author discusses various approaches to estimating summary characteristics of a stationary point process from its \(n\) independent copies observed through possibly different observation windows. The individual estimators within each window can be averaged (possibly with weights) or they can be pooled, e.g., for ratio unbiased estimators one can take the sums of numerators and denominators in individual windows. The author compares estimators based on their integrated square error for three basic types of point processes: Poisson process, Thomas process (exhibiting clustering) and Matérn hard-core process. It is found that the most appropriate way of pooling depends on the particular summary characteristics, the chosen edge-correction method and also on the type of the point process. The methods are applied to a replicated dataset from forestry.
MSC:
62M09 Non-Markovian processes: estimation
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
62M30 Inference from spatial processes
62G05 Nonparametric estimation
Software:
spatstat; R
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References:
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