ON A SINGULARITY OCCURRING IN A SELF-CORRECTING POINT PROCESS MODEL

HARALD LUSCHGY

Institute of Mathematical Statistics, University of Münster, Einsteinstr. 62, D-4400 Münster, Germany

(Received September 24, 1991; revised October 26, 1992)

Abstract. 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.

Key words and phrases: Self-correcting point process, locally asymptotically quadratic model, locally asymptotically Brownian functional, ML-estimator, nonnormal limiting distribution.