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.

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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.