Abstract: This article discusses estimation of the mean function of point processes when only incomplete data are available. Specifically, we consider situations in which each individual who gives rise to a point process is observed only at discrete time points and no information about the histories of the subject between observation times is available. Data structures of this type occur, for example, in many clinical trials and reliability studies in which it is impractical to keep subjects under observation over the entire study period. The main difficulty in estimating the mean function in such situations is that observation times usually differ between study subjects. In this paper, a simple and consistent estimator of the mean function of point processes is presented. Following two illustrative examples, a small simulation study demonstrates that the presented estimator is satisfactory in the cases considered.
Key words and phrases: Mean function, panel count data, point process, isotonic regression.