Inference for thinned point processes, with application to Cox processes

Alan F. Karr

Journal of Multivariate Analysis, 1985, vol. 16, issue 3, 368-392

Abstract: Given i.i.d. point processes N1, N2,..., let the observations be p-thinnings N'1, N'2,..., where p is a function from the underlying space E (a compact metric space) to [0, 1], whose interpretation is that a point of Ni at x is retained with probability p(x) and deleted with probability 1-p(x). Strongly consistent estimators of the thinning function p and the Laplace functional LN(f) = E[e-N(f)] of the Ni are constructed; associated "central limit" properties are given. Tests are presented, for the case when the Ni and N'i are both observable, of the hypothesis that the N'i are p-thinnings of the Ni. State estimation techniques are developed for the case where the Ni are Cox processes directed by unobservable random measures Mi; these techniques yield minimum mean-squared error estimators, based on observation of only the thinned processes N'i of the Ni and the directing measures Mi. Limit theorems for empirical Laplace functionals of point processes are given.

Keywords: point; process; thinned; point; process; inference; for; point; processes; Cox; process; state; estimation; for; Cox; processes; empirical; Laplace; functional; consistency; asymptotic; normality (search for similar items in EconPapers)
Date: 1985
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/0047-259X(85)90026-0
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:16:y:1985:i:3:p:368-392

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Journal of Multivariate Analysis is currently edited by de Leeuw, J.

More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Catherine Liu ().