Towards optimal Takacs--Fiksel estimation

TL;DR

This paper proposes a new method for selecting weight functions in the Takacs--Fiksel estimation of spatial Gibbs point processes, aiming to improve efficiency over pseudolikelihood, demonstrated through real data and simulations.

Contribution

It introduces a general procedure to optimize weight functions in Takacs--Fiksel estimation, reducing Godambe information and enhancing estimation accuracy.

Findings

The new method outperforms pseudolikelihood in certain datasets.

Application to neuroscience data shows improved parameter estimation.

Simulation results confirm efficiency gains of the proposed approach.

Abstract

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 new procedure is applied to a standard dataset and to a recent neuroscience replicated point pattern dataset. Finally, the performance of the new procedure is investigated in a simulation study.