Negative dependence in sampling
Journal article, 2012

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.

Pareto sampling

Sampford sampling

uniform spanning tree

Rayleigh property


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Royal Institute of Technology (KTH)

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Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Scandinavian Journal of Statistics

0303-6898 (ISSN) 1467-9469 (eISSN)

Vol. 39 4 830-838

Areas of Advance

Information and Communication Technology


Basic sciences

Subject Categories

Probability Theory and Statistics



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