On a singularity occurring in a self-correcting point process model

In a self-correcting point process model a boundary point of the parameter set is shown to be singular. This means a local behavior of the model which is qualitatively different from the LAN (or LAMN) condition satisfied at the other parameter points. As a consequence we obtain a nonnormal limiting distribution of the ML-estimator normalized with the random Fisher information.Work supported by a Heisenberg grant of the Deutsche Forschungsgemeinschaft.