Semiparametric Estimation in Regression Models for Point Processes based on One Realization

We are dealing with regression models for point processes having a multiplicative intensity process of the form alpha(t) * b_t . The deterministic function alpha describes the long-term trend of the process. The stochastic process b accounts for the short-term random variations and depends on a finite-dimensional parameter. The semiparametric estimation procedure is based on one single observation over a long time interval. We will use penalized estimation functions to estimate the trend alpha, while the likelihood approach to point processes is employed for the parametric part of the problem. Our methods are applied to earthquake data as well as to records on 24-hours ECG