Electronic Journal of Statistics

Maximum pseudolikelihood estimator for exponential family models of marked Gibbs point processes

Jean-Michel Billiot, Jean-François Coeurjolly, and Rémy Drouilhet

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Abstract

This paper is devoted to the estimation of a vector θ parametrizing an energy function of a Gibbs point process, via the maximum pseudolikelihood method. Strong consistency and asymptotic normality results of this estimator depending on a single realization are presented. In the framework of exponential family models, sufficient conditions are expressed in terms of the local energy function and are verified on a wide variety of examples.

Article information

Source
Electron. J. Statist., Volume 2 (2008), 234-264.

Dates
First available in Project Euclid: 23 April 2008

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1208958317

Digital Object Identifier
doi:10.1214/07-EJS160

Mathematical Reviews number (MathSciNet)
MR2399195

Zentralblatt MATH identifier
1135.62364

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

Keywords
stationary marked Gibbs point processes pseudolikelihood method minimum contrast estimators

Citation

Billiot, Jean-Michel; Coeurjolly, Jean-François; Drouilhet, Rémy. Maximum pseudolikelihood estimator for exponential family models of marked Gibbs point processes. Electron. J. Statist. 2 (2008), 234--264. doi:10.1214/07-EJS160. https://projecteuclid.org/euclid.ejs/1208958317


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