Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/157009
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dc.contributor.authorPrivault, Nicolasen_US
dc.date.accessioned2022-04-29T06:07:02Z-
dc.date.available2022-04-29T06:07:02Z-
dc.date.issued2021-
dc.identifier.citationPrivault, N. (2021). Cardinality estimation for random stopping sets based on Poisson point processes. ESAIM: Probability and Statistics, 25, 87-108. https://dx.doi.org/10.1051/ps/2021004en_US
dc.identifier.issn1292-8100en_US
dc.identifier.urihttps://hdl.handle.net/10356/157009-
dc.description.abstractWe construct unbiased estimators for the distribution of the number of points inside random stopping sets based on a Poisson point process. Our approach is based on moment identities for stopping sets, showing that the random count of points inside the complement S¯ of a stopping set S has a Poisson distribution conditionally to S. The proofs do not require the use of set-indexed martingales, and our estimators have a lower variance when compared to standard sampling. Numerical simulations are presented for examples such as the convex hull and the Voronoi flower of a Poisson point process, and their complements.en_US
dc.description.sponsorshipMinistry of Education (MOE)en_US
dc.language.isoenen_US
dc.relationMOE2018-T1-001-201 (RG25/18)en_US
dc.relation.ispartofESAIM: Probability and Statisticsen_US
dc.rights© 2021 EDP Sciences, SMAI. All rights reserved. This paper was published in ESAIM: Probability and Statistics and is made available with permission of EDP Sciences, SMAI.en_US
dc.subjectScience::Mathematicsen_US
dc.titleCardinality estimation for random stopping sets based on Poisson point processesen_US
dc.typeJournal Articleen
dc.contributor.schoolSchool of Physical and Mathematical Sciencesen_US
dc.identifier.doi10.1051/ps/2021004-
dc.description.versionSubmitted/Accepted versionen_US
dc.identifier.scopus2-s2.0-85103344024-
dc.identifier.volume25en_US
dc.identifier.spage87en_US
dc.identifier.epage108en_US
dc.subject.keywordsStochastic Ggeometryen_US
dc.subject.keywordsPoisson Point Processen_US
dc.description.acknowledgementThis research is supported by the Ministry of Education, Singapore, under its Tier 1 Grant MOE2018-T1-001-201 RG25/18.en_US
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