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

Mathematics – Statistics Theory

Scientific paper

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Published in at http://dx.doi.org/10.1214/07-EJS160 the Electronic Journal of Statistics (http://www.i-journals.org/ejs/) by t

Scientific paper

10.1214/07-EJS160

This paper is devoted to the estimation of a vector $\bm {\theta}$ 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.

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