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Negative Dependence in Sampling
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0003-1055-1474
2012 (English)In: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 39, no 4, 830-838 p.Article in journal (Refereed) Published
Abstract [en]

. The strong Rayleigh property is a new and robust negative dependence property that implies negative association; in fact it implies conditional negative association closed under external fields (CNA+). Suppose that and are two families of 0-1 random variables that satisfy the strong Rayleigh property and let . We show that {Zi} conditioned on is also strongly Rayleigh; this turns out to be an easy consequence of the results on preservation of stability of polynomials of Borcea & Branden (Invent. Math., 177, 2009, 521569). This entails that a number of important pps sampling algorithms, including Sampford sampling and Pareto sampling, are CNA+. As a consequence, statistics based on such samples automatically satisfy a version of the Central Limit Theorem for triangular arrays.

Place, publisher, year, edition, pages
2012. Vol. 39, no 4, 830-838 p.
Keyword [en]
Pareto sampling, Rayleigh property, Sampford sampling, uniform spanning tree
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-109178DOI: 10.1111/j.1467-9469.2011.00766.xISI: 000311396200016Scopus ID: 2-s2.0-84870063383OAI: oai:DiVA.org:kth-109178DiVA: diva2:582812
Funder
Knut and Alice Wallenberg FoundationSwedish Research Council
Note

QC 20121307

Available from: 2013-01-07 Created: 2012-12-21 Last updated: 2017-12-06Bibliographically approved

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Brändén, Petter

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