Estimation of the local intensity of a cyclic Poisson process by means of nearest neighbor distances

MANGKU, I W.

MILANG Journal of Mathematics and Its Applications
Vol. 1 No. 1 (2002): Journal of Mathematics and Its Applications

We consider the problem of estimating the local intensity of a cyclic Poisson point process, when we know the period. 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 local intensity at a given point. A nearest neighbor estimator of the local intensity is proposed, and we show that our estimator is weakly and strongly consistent, as the window expands.