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The BK inequality for pivotal sampling a.k.a. the Srinivasan samplig process


 
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1. Title Title of document The BK inequality for pivotal sampling a.k.a. the Srinivasan samplig process
 
2. Creator Author's name, affiliation, country Johan Jonasson; Chalmers University of Technology; Sweden
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) Srinivasan sampling, negative association, Reimer's inequality
 
3. Subject Subject classification 60C05 ; 60K35
 
4. Description Abstract The pivotal sampling algorithm, a.k.a. the Srinivasan sampling process, is a simply described recursive algorithm for sampling from a finite population a fixed number of items such that each item is included in the sample with a prescribed desired inclusion probability.The algorithm has attracted quite some interest in recent years due to the fact that despite its simplicity, it has been shown to satisfy strong properties of negative dependence, e.g. conditional negative association.In this paper it is shown that (tree-ordered) pivotal/Srinivasan sampling also satisfies the BK inequality.This is done via a mapping from increasing sets of samples to sets of match sequencesand an application of the van den Berg-Kesten-Reimer inequality.The result is one of only very few non-trivial situations where the BK inequality is known to hold.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) The Knut and Alice Wallenberg Foundation
 
7. Date (YYYY-MM-DD) 2013-05-16
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/2045
 
10. Identifier Digital Object Identifier 10.1214/ECP.v18-2045
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 18
 
12. Language English=en en
 
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