Maximum likelihood for the fully observed contact process

The contact process—and more generally interacting particle systems—are useful and interesting models for a variety of statistical problems. This paper is concerned with maximum likelihood estimation of the parameters of the process for the case where the process is supercritical, starts with a single infected site at the origin and is observed during a long time interval [0,t][0,t]. We construct the estimators and prove their consistency and asymptotic normality as t→∞t→∞. We also discuss the relation with the estimation problem for the process observed at a single large time.