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Negative dependence in sampling

Petter Brändén ; Johan Jonasson (Institutionen för matematiska vetenskaper, matematik)
Scandinavian Journal of Statistics (0303-6898). Vol. 39 (2012), 4, p. 830-838.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: Pareto sampling, Rayleigh property, Sampford sampling, uniform spanning tree



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Denna post skapades 2011-12-06. Senast ändrad 2016-08-19.
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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

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Informations- och kommunikationsteknik
Matematisk statistik

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