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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:Network driven sampling\; a critical threshold for
design effects - Karl Rohe (University of Wiscons
in-Madison)
DTSTART;TZID=Europe/London:20160715T140000
DTEND;TZID=Europe/London:20160715T143000
UID:TALK66776AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/66776
DESCRIPTION:Web crawling and respondent-driven sampling (RDS)
are two types of network driven sampling technique
s that are popular when it is difficult to contact
individuals in the population of interest. This p
aper studies network driven sampling as a Markov p
rocess on the social network that is indexed by a
tree. Each node in this tree corresponds to an obs
ervation and each edge in the tree corresponds to
a referral. Indexing with a tree\, instead of a ch
ain\, allows for the sampled units to refer multip
le future units into the sample. In survey samplin
g\, the design effect characterizes the additional
variance induced by a novel sampling strategy. If
the design effect is $D$\, then constructing an e
stimator from the novel design makes the variance
of the estimator $D$ times greater than it would b
e under a simple random sample. Under \;certai
n assumptions on the referral tree\, the design ef
fect of network driven sampling has a critical thr
eshold that is a function of the referral rate $m$
and the clustering structure in the social networ
k\, represented by the second eigenvalue of the Ma
rkov transition matrix $\\lambda_2$. If $m < 1/\\l
ambda_2^2$\, then the design effect is finite (i.e
. the standard estimator is $\\sqrt{n}$-consistent
). However\, if $m > 1/\\lambda_2^2$\, then the de
sign effect grows with $n$ (i.e. the standard esti
mator is no longer $\\sqrt{n}$-consistent\; it con
verges at the slower rate of $\\log_m \\lambda_2$)
.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:info@newton.ac.uk
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