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Abstract: This paper studies a method to estimate the parameters governing thedistribution of a stationary marked Gibbs point process. This procedure, knownas the Takacs-Fiksel method, is based on the estimation of the left and righthand sides of the Georgii-Nguyen-Zessin formula and leads to a family ofestimators due to the possible choices of test functions. We propose severalexamples illustrating the interest and flexibility of this procedure. We alsoprovide sufficient conditions based on the model and the test functions toderive asymptotic properties consistency and asymptotic normality of theresulting estimator. The different assumptions are discussed for exponentialfamily models and for a large class of test functions. A short simulation studyis proposed to assess the correctness of the methodology and the asymptoticresults.



Autor: Jean-François Coeurjolly GIPSA-lab, LJK, David Dereudre LAMAV, Rémy Drouilhet LJK, Frédéric Lavancier LMJL

Fuente: https://arxiv.org/







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