Asymptotic Properties of Estimators for the Parameters of Spatial Inhomogeneous Poisson Point Processes

Consider a spatial point pattern realized from an inhomogeneous Poisson process on a bounded Borel set , with intensity function . (s; .), where . In this article, we show that the maximum likelihood estimator and the Bayes estimator are consistent, asymptotically normal, and asymptotically efficient as the sample region . These results extend asymptotic results of Kutoyants (1984), proved for an inhomogeneous Poisson process on [0, T] , where T ... They also formalize (and extend to the multiparameter case) results announced by Krickeberg (1982), for the spatial domain . Furthermore, a Cramér.Rao lower bound is found for any estimator of .. The asymptotic properties of and are considered for modulated (Cox (1972)), and linear Poisson processes.