Negative Dependence and Srinivasan's Sampling Process
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.
MSU Digital Commons Citation
Kramer, Josh Brown; Cutler, Jonathan; and Radcliffe, A. J., "Negative Dependence and Srinivasan's Sampling Process" (2011). Department of Mathematics Facuty Scholarship and Creative Works. 110.