Maximum Likelihood Estimation in the Multiplicative Intensity Model: A Survey
本文综述了直线简单点过程的非参数乘法强度模型，通过引入拓扑扩展处理多点过程，确定了最大似然估计量并与Aalen估计量比较，用泊松过程、删失生存数据和Cox回归模型示例说明。
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.