Non-parametric inference for stationary pairwise interaction point process
Résumé
Among models, allowing to introduce interaction between points, we find the large class of Gibbs models of spatial point processes coming from
statistical physics. Such models can produce repulsive as well as attractive point pattern. In this paper, we focus on the main class of Gibbs models which is the class of pairwise interaction point processes characterized by the Papangelou conditional intensity. We suggest a new non-parametric estimate of the pairwise interaction function in the Papangelou conditional intensity for stationary pairwise interaction point process. An order bound for the bias of the resulting estimator is given. Strong uniform consistency is established by a class of stationary Gibbs random fields and the finite range property.
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