Towards optimal Takacs--Fiksel estimation

The Takacs--Fiksel method is a general approach to estimate the parameters of a spatial Gibbs point process. This method embraces standard procedures such as the pseudolikelihood and is defined via weight functions. In this paper we propose a general procedure to find weight functions which reduce the Godambe information and thus outperform pseudolikelihood in certain situations. The performance of the new procedure is investigated in a simulation study and it is applied to a standard dataset. Finally, we extend the procedure to handle replicated point patterns and apply it to a recent neuroscience dataset.