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.