Marked Gibbs Processes and Asymptotic Normality of Maximum Pseudo-Likelihood Estimators

Abstract

This paper discusses the concept of marked stationary Gibbs processes which are globally defined on the continuous state space Rν and an arbitrary mark space M. The framework is the theory of superstable potential Gibbs processes of Ruelle [13]. The maximum pseudo-likelihood estimator of marked potentials and its strong consistency are considered. Finally the asymptotic normality of maximum pseudo-likelihood estimators for the finite-range marked potential case is shown, which is an extension of Jensen & Künsch (1994).