Optimisation of linear unbiased intensity estimators for point processes

Mrkvicka, Tomás; Molchanov, Ilya (2005). Optimisation of linear unbiased intensity estimators for point processes. Annals of the Institute of Statistical Mathematics, 57(1), pp. 71-81. Springer 10.1007/BF02506880

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A general non-stationary point process whose intensity function is given up to unknown numerical factor λ is considered. As an alternative to the conventional estimator of λ based on counting the points, we consider general linear unbiased estimators of λ given by sums of weights associated with individual points. A necessary and sufficient condition for a linear, unbiased estimator for the intensity λ to have the minimum variance is determined. It is shown that there are “nearly” no other processes than Poisson and Cox for which the unweighted estimator of λ, which counts the points only, is optimal. The properties of the optimal estimator are illustrated by simulations for the Matérn cluster and the Matérn hard-core processes.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science

UniBE Contributor:

Molchanov, Ilya

Subjects:

500 Science > 510 Mathematics

ISSN:

0020-3157

Publisher:

Springer

Language:

English

Submitter:

Ilya Molchanov

Date Deposited:

09 Aug 2016 07:43

Last Modified:

09 Aug 2016 07:43

Publisher DOI:

10.1007/BF02506880

BORIS DOI:

10.7892/boris.85373

URI:

https://boris.unibe.ch/id/eprint/85373

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