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Asymptotic Gaussianity of some estimators for reduced factorial moment measures and product densities of stationary Poisson cluster processes. (English) Zbl 0666.62032
The asymptotic normality of a class of estimators related to reduced factorial moment measures is established, using the central limit theorem in which the moment conditions are reduced to a minimum. The weak convergence theorem is also provided in the case of a stationary simple Poisson cluster process (pcp) and is applied to the investigation of the asymptotic behaviour of the empirical second-order moment function. Further, the asymptotic properties of kernel-type estimators for second- order product densities of pcp’s are discussed.
Reviewer: M.Akahira

MSC:
62F12 Asymptotic properties of parametric estimators
60F05 Central limit and other weak theorems
60F17 Functional limit theorems; invariance principles
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
Software:
spatial
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