Survival models and martingale dynamics. (English) Zbl 0688.62053

Arjas, Elja

Scand. J. Stat. 16, No. 3, 177-225 (1989).

Summary: This paper reviews some ideas and techniques which appear central in the statistical modelling of longitudinal observational data. The presentation is based entirely on the framework of marked point processes, with an emphasis on the dynamical aspects of the modelling. The concepts of hazard and prediction are given special attention, together with the information which forms their natural basis. Finally, we discuss a number of structural questions relating to likelihood-based inference from marked point processes.

MSC:

62M99	Inference from stochastic processes
60G55	Point processes (e.g., Poisson, Cox, Hawkes processes)

Keywords:

filtering; event history analysis; partial model specification; unobservable random variation; review; statistical modelling of longitudinal observational data; marked point processes; hazard; prediction; likelihood-based inference