Consistent Estimation of the Intensity Function of a Cyclic Poisson Process.211 Probability, Networks and Algorithms

摘要

We construct and investigate a consistent kernel-type nonparametric estimator of211u001ethe intensity function of a cyclic Poisson process when the period is unknown. We 211u001eassume that only a single realization of the Poisson process is observed in a 211u001ebounded window. In particular, we prove that the proposed estimator is weakly and 211u001estrongly consistent when the size of the window expands.