Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/157009
Title: Cardinality estimation for random stopping sets based on Poisson point processes
Authors: Privault, Nicolas
Keywords: Science::Mathematics
Issue Date: 2021
Source: Privault, 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/2021004
Project: MOE2018-T1-001-201 (RG25/18)
Journal: ESAIM: Probability and Statistics
Abstract: We 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.
URI: https://hdl.handle.net/10356/157009
ISSN: 1292-8100
DOI: 10.1051/ps/2021004
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.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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