Open AccessEstimation of the local intensity of a cyclic Poisson process by means of nearest neighbor distances
Author(s) -
I Wayan Mangku
Publication year - 2002
Publication title -
journal of mathematics and its applications jma
Language(s) - English
Resource type - Journals
ISSN - 1412-677X
DOI - 10.29244/jmap.1.1.1-12
Subject(s) - estimator , poisson distribution , point process , k nearest neighbors algorithm , intensity (physics) , poisson point process , mathematics , poisson process , bounded function , point (geometry) , window (computing) , poisson regression , statistics , mathematical analysis , computer science , physics , artificial intelligence , geometry , optics , operating system , population , demography , sociology
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.