The class of Gibbs Point Processes (GPPs) is a large class of spatial point processes that can model both clustered and repulsive point patterns. They are specified by the point pattern $\mathbf{x}$ and the conditional strength of the location $u$. Roughly speaking, it is the probability of an event occurring in a microsphere around u given the rest of the configuration. $\mathbf{x}$. The simplest and most natural class of models is that of pairwise interacting point processes whose conditional strength depends on the number of points and the pairwise distance between them. This paper is concerned with the problem of nonparametric estimation of pairwise interaction functions. We propose to estimate using the orthogonal series expansion of its logarithm. Such an approach has many advantages over existing approaches. The estimation procedure is simple, fast, and completely data-driven. We provide asymptotic properties such as consistency and asymptotic normality, demonstrate the efficiency of the procedure through simulation experiments, and illustrate on several datasets.

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