# Asymptotic properties of the maximum pseudo-likelihood estimator for stationary Gibbs point processes including the Lennard-Jones model

Abstract : This paper presents asymptotic properties of the maximum pseudo-likelihood estimator of a vector $\Vect{\theta}$ parameterizing a stationary Gibbs point process. Sufficient conditions, expressed in terms of the local energy function defining a Gibbs point process, to establish strong consistency and asymptotic normality results of this estimator depending on a single realization, are presented.These results are general enough to no longer require the local stability and the linearity in terms of the parameters of the local energy function. We consider characteristic examples of such models, the Lennard-Jones and the finite range Lennard-Jones models. We show that the different assumptions ensuring the consistency are satisfied for both models whereas the assumptions ensuring the asymptotic normality are fulfilled only for the finite range Lennard-Jones model.
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https://hal.archives-ouvertes.fr/hal-00442750
Contributor : Jean-François Coeurjolly <>
Submitted on : Monday, July 12, 2010 - 1:21:44 PM
Last modification on : Thursday, November 19, 2020 - 1:01:06 PM
Long-term archiving on: : Thursday, October 14, 2010 - 3:32:39 PM

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Jean-François Coeurjolly, Rémy Drouilhet. Asymptotic properties of the maximum pseudo-likelihood estimator for stationary Gibbs point processes including the Lennard-Jones model. Electronic journal of statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2010, 4, pp.677-706. ⟨10.1214/09-EJS494⟩. ⟨hal-00442750v2⟩

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