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

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

Author(s) -

Granville V.

Publication year - 1998

Publication title -

statistica neerlandica

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.52

H-Index - 39

eISSN - 1467-9574

pISSN - 0039-0402

DOI - 10.1111/1467-9574.00071

Subject(s) - mathematics , k nearest neighbors algorithm , poisson distribution , estimator , logarithm , poisson point process , intensity (physics) , euclidean distance , point process , simple (philosophy) , combinatorics , mathematical analysis , statistics , physics , geometry , computer science , artificial intelligence , optics , philosophy , epistemology

A new unbiased consistent asymptotically normal estimator U k of the intensity λ of a stationary multivariate Poisson point process is exhibited. This estimate is based on a combination of the j ‐th nearest neighbor (possibly non Euclidean) distances ( j =1, ..., k ) to a single fixed site x . A simple closed form containing logarithmic terms is obtained for E ( U l k )(0< l < k ).

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