Piecewise pseudo estimation for NHPP using data in the adjacent intervals

In modeling a system with NHPP, we generally need to estimate the parameters of its mean function Λ(t). In practical situations, however, there exist many cases that the parametric representation of Λ(t) is unknown. For such a case, Law and Kelton proposed a nonparametric estimation with a piecewise-constant intensity function, which requires many sample data sets to obtain statistically accurate values. In this paper we propose a piecewise estimation method which covers the case that only one or a few sets of sample data can be obtained. The proposed method gives pseudo estimator by using the sample data of the adjacent intervals, nevertheless it can theoretically gain more statistical accuracy even with one or a few sets of sample data than the method by Law and Kelton. The effectiveness of the proposed method is shown by some experimental results.