# On asymptotic normality of nonparametric estimate for a stationary pairwise interaction point process

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1 FIGAL - Fiabilité et Géométrie Aléatoire
LJK - Laboratoire Jean Kuntzmann
Abstract : We prove the asymptotic normality of nonparametric estimator of pairwise interaction function for a stationary pairwise interaction point process characterized by the Papangelou conditional intensity and observed in a bounded window of a sequence of cubes growing up to $\mathbb{R}^d$. Formula for the variance of the resulting estimator can be obtained using Papangelou conditional intensity of the point process. This is a random function satisfying the counterpart of the Georgii-Nguyen-Zessin formula. The proof of the asymptotic normality of the resulting estimator is based on the $m_n$-approximation method in the setting of dependent random fields indexed by $\mathbb{Z}^d$ where $d$ is a positive integer.
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Cited literature [40 references]

https://hal.inria.fr/hal-01121114
Submitted on : Wednesday, March 23, 2016 - 1:03:32 PM
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• HAL Id : hal-01121114, version 3

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Nadia Morsli. On asymptotic normality of nonparametric estimate for a stationary pairwise interaction point process. 2015. ⟨hal-01121114v3⟩

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