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Negative Dependence and Srinivasan's Sampling Process

Published online by Cambridge University Press:  22 February 2011

JOSH BROWN KRAMER
Affiliation:
Department of Mathematics and Computer Science Department, Illinois Wesleyan University, Bloomington, IL, USA (e-mail: jbrownkr@iwu.edu)
JONATHAN CUTLER
Affiliation:
Department of Mathematical Sciences, Montclair State University, Montclair, NJ, USA (e-mail: jonathan.cutler@montclair.edu)
A. J. RADCLIFFE
Affiliation:
Department of Mathematics, University of Nebraska–Lincoln, Lincoln, NE, USA (e-mail: aradcliffe1@math.unl.edu)

Abstract

Dubhashi, Jonasson and Ranjan Dubhashi, Jonasson and Ranjan (2007) study the negative dependence properties of Srinivasan's sampling processes (SSPs), random processes which sample sets of a fixed size with prescribed marginals. In particular they prove that linear SSPs have conditional negative association, by using the Feder–Mihail theorem and a coupling argument. We consider a broader class of SSPs that we call tournament SSPs (TSSPs). These have a tree-like structure and we prove that they have conditional negative association. Our approach is completely different from that of Dubhashi, Jonasson and Ranjan. We give an abstract characterization of TSSPs, and use this to deduce that certain conditioned TSSPs are themselves TSSPs. We show that TSSPs have negative association, and hence conditional negative association. We also give an example of an SSP that does not have negative association.

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Paper
Copyright
Copyright © Cambridge University Press 2011

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References

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