  Second-order statistics play a crucial role in analysing point processes.
Previous research has specifically explored locally weighted second-order
statistics for point processes, offering diagnostic tests in various spatial
domains. However, there remains a need to improve inference for complex
intensity functions, especially when the point process likelihood is
intractable and in the presence of interactions among points. This paper
addresses this gap by proposing a method that exploits local second-order
characteristics to account for local dependencies in the fitting procedure. Our
approach utilises the Papangelou conditional intensity function for general
Gibbs processes, avoiding explicit assumptions about the degree of interaction
and homogeneity. We provide simulation results and an application to real data
to assess the proposed method's goodness-of-fit. Overall, this work contributes
to advancing statistical techniques for point process analysis in the presence
of spatial interactions.
