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The class of Gibbs point processes (GPP) is a large class of spatial pointprocesses able to model both clustered and repulsive point patterns. They arespecified by their conditional intensity, which for a point pattern$\mathbf{x}$ and a location $u$, is roughly speaking the probability that anevent occurs in an infinitesimal ball around $u$ given the rest of theconfiguration is $\mathbf{x}$. The most simple and natural class of models isthe class of pairwise interaction point processes where the conditionalintensity depends on the number of points and pairwise distances between them.This paper is concerned with the problem of estimating the pairwise interactionfunction non parametrically. We propose to estimate it using an orthogonalseries expansion of its logarithm. Such an approach has numerous advantagescompared to existing ones. The estimation procedure is simple, fast andcompletely data-driven. We provide asymptotic properties such as consistencyand asymptotic normality and show the efficiency of the procedure throughsimulation experiments and illustrate it with several datasets.

Pairwise interaction function estimation of Gibbs point processes using basis expansion