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Preprints, Working Papers, ... Year : 2015

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

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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Dates and versions

hal-01121114 , version 1 (27-02-2015)
hal-01121114 , version 2 (29-04-2015)
hal-01121114 , version 3 (23-03-2016)

Identifiers

  • HAL Id : hal-01121114 , version 3

Cite

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