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


Petter Brändén

Royal Institute of Technology (KTH)

Johan Jonasson

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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