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UID:2950@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20190527T140000
DTEND;TZID=Europe/Paris:20190527T150000
DTSTAMP:20190512T120000Z
URL:https://www.i2m.univ-amu.fr/evenements/exponential-inequalities-for-sa
 mpling-designs/
SUMMARY: (...): Exponential inequalities for sampling designs
DESCRIPTION:: Exponential concentration inequalities are helpful to guarant
 y that the difference between a parameter and its estimator is no greater 
 than a given threshold\, with probability tending exponentially fast to 1 
 as the sample size increases. Such inequalities are in particular helpful 
 in streaming algorithms\, when a sample is obtained in one pass of the fil
 e only\, and when so-called epsilon-delta approximations are wanted. In a 
 recent work\, Bertail and Clemencon (2019) obtained a general exponential 
 inequality for negatively associated sampling designs\, a family including
  rejective sampling\, Rao-Sampford sampling and pivotal sampling. In this 
 work\, we define what we call the generalized Sen-Yates-Grundy conditions.
  Making use of a martingale characterization\, we prove that under these c
 onditions the Horvitz-Thompson estimator satisfies a version of the Azuma-
 Hoeffding therem. These conditions hold true for rejective sampling\, Chao
 's sampling\, Tille's eliminatory procedure and the generalized Midzuno me
 thod\, for example.This is joint work with Mathieu Gerber (University of B
 ristol).http://www.ensai.fr/enseignant/alias/guillaume-chauvet.html
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