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ON A SINGULARITY OCCURRING IN

A SELF-CORRECTING POINT PROCESS MODEL

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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.

**Source**
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