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Maximum pseudolikelihood estimator for exponential family models of marked Gibbs point processes. (English) Zbl 1135.62364

Summary: This paper is devoted to the estimation of a vector \(\theta \) 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.

MSC:

62M09 Non-Markovian processes: estimation
62G20 Asymptotic properties of nonparametric inference
60G55 Point processes (e.g., Poisson, Cox, Hawkes processes)
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