(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.
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