Electronic Journal of Statistics

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

Jean-François Coeurjolly and Rémy Drouilhet

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Abstract

This paper presents asymptotic properties of the maximum pseudo-likelihood estimator of a vector 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.

Article information

Source
Electron. J. Statist., Volume 4 (2010), 677-706.

Dates
First available in Project Euclid: 9 August 2010

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1281358966

Digital Object Identifier
doi:10.1214/09-EJS494

Mathematical Reviews number (MathSciNet)
MR2678967

Zentralblatt MATH identifier
1329.62108

Subjects
Primary: 60G55: Point processes
Secondary: 60J25: Continuous-time Markov processes on general state spaces

Keywords
Stationary Gibbs point processes maximum pseudo-likelihood estimator Lennard-Jones model

Citation

Coeurjolly, Jean-François; Drouilhet, Rémy. Asymptotic properties of the maximum pseudo-likelihood estimator for stationary Gibbs point processes including the Lennard-Jones model. Electron. J. Statist. 4 (2010), 677--706. doi:10.1214/09-EJS494. https://projecteuclid.org/euclid.ejs/1281358966


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