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Negative Dependence in Sampling
Author(s) -
BRÄNDÉN PETTER,
JONASSON JOHAN
Publication year - 2012
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2011.00766.x
Subject(s) - mathematics , sampling (signal processing) , property (philosophy) , stability (learning theory) , central limit theorem , rayleigh scattering , combinatorics , limit (mathematics) , pareto principle , discrete mathematics , statistics , mathematical analysis , computer science , quantum mechanics , physics , epistemology , filter (signal processing) , machine learning , computer vision , philosophy
. 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 { Z i } 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 & Brändén ( Invent. Math. , 177, 2009, 521–569). This entails that a number of important π ps 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.