Abstract
Summary The nonparametric multiplicative intensity model for simple point processes on the line is considered. By introducing a suitable topology on the space of all point process paths, a topological extension of the model is found, accommodating point processes with multiple points. In the extended model the maximum likelihood estimator is determined and shown to be interpretable in terms of a multiple point process. Finally, the maximum likelihood estimator and the Aalen estimator are compared. The results are illustrated by examples involving a model for Poisson processes, a model for censored survival data and the Cox regression model.
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