Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

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

Nadia Morsli 1, *
* Corresponding author
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.
Document type :
Preprints, Working Papers, ...
Complete list of metadata

Cited literature [40 references]  Display  Hide  Download

https://hal.inria.fr/hal-01121114
Contributor : Nadia Morsli <>
Submitted on : Wednesday, March 23, 2016 - 1:03:32 PM
Last modification on : Thursday, November 19, 2020 - 1:01:17 PM
Long-term archiving on: : Friday, June 24, 2016 - 1:24:37 PM

File

asympto-stationnaire-HAL.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01121114, version 3

Collections

Citation

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

Share

Metrics

Record views

241

Files downloads

352