We consider the problem of estimating the intensity function of a cyclic Poisson point process. We suppose that only a single realization of the cyclic Poisson point process is observed within a bounded 'window', and our aim is to estimate consistently the intensity function at a given point. A nearest neighbor estimator of the intensity function is proposed, and we show that our estimator is weakly and strongly consistent, as the window expands.

Point processes (msc 60G55), Estimation (msc 62G05), Asymptotic properties (msc 62G20)
CWI
CWI. Probability, Networks and Algorithms [PNA]
Stochastic Dynamics and Discrete Probability

Mangku, I.W. (1999). Nearest neighbor estimation of the intensity function of a cyclic Poisson process. CWI. Probability, Networks and Algorithms [PNA]. CWI.