Towards optimal Takacs–Fiksel estimation

Jean-François Coeurjolly (1) , Yongtao Guan (2) , Mahdieh Khanmohammadi (3) , Rasmus Waagepetersen (4)

1 FIGAL - Fiabilité et Géométrie Aléatoire
2 University of Miami School of Business
3 DIKU - Department of Computer Science [Copenhagen]
4 Department of Mathematical Sciences [Aalborg]

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.

Mots clés: pseudolikelihood; spatial point processes; Gibbs point processes; Godambe information; optimal estimation

Domaines: Statistiques [math.ST]

Jean-François Coeurjolly, Yongtao Guan, Mahdieh Khanmohammadi, Rasmus Waagepetersen. Towards optimal Takacs–Fiksel estimation. 2015. ⟨hal-01247097v1⟩