Negative dependence in sampling
Artikel i vetenskaplig tidskrift, 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

Författare

Petter Brändén

Kungliga Tekniska Högskolan (KTH)

Johan Jonasson

Chalmers, Matematiska vetenskaper, Matematik

Göteborgs universitet

Scandinavian Journal of Statistics

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

Vol. 39 830-838

Styrkeområden

Informations- och kommunikationsteknik

Fundament

Grundläggande vetenskaper

Ämneskategorier

Sannolikhetsteori och statistik

DOI

10.1111/j.1467-9469.2011.00766.x