Asymptotic Properties of Takacs-Fiksel Estimation Method for GIBBS Point Processes

Abstract

A Takacs-Fiksel type estimator is proposed for stationary Gibbs point processes when many independent realizations are available. Strong consistency and asymptotic normality of this estimator are proved. Furthermore, strong consistency of the estimator is obtained in the single realization case.

Keywords:

• Gibbs point processes
• interaction potential
• Takacs-Fiksel estimation method
• consistency
• asymptotic normality