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

I Wayan Mangku | Zendy

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Estimation 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 -

milang journal of mathematics and its applications

Language(s) - English

Resource type - Journals

ISSN - 2963-5233

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.

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