A Note on Estimation of the Global Intensity of a Cyclic Poisson Process in the Presence of Linear Trend

We construct and investigate a consistent kernel-type nonparametric estimator of the global intensity of a cyclic Poisson process in the presence of linear trend. It is assumed that only a single realization of the Poisson process is observed in a bounded window. We prove that the proposed estimator is consistent when the size of the window indefinitely expands. The asymptotic bias and variance of the proposed estimator are computed. Bias reduction of the estimator is also proposed.1991 Mathematics Subject Classification: 6