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arxiv: 1309.4029 · v2 · pith:XO6X6HQTnew · submitted 2013-09-16 · 🧮 math.ST · stat.TH

Concentration inequalities for sampling without replacement

R\'emi Bardenet , Odalric-Ambrym Maillard This is my paper
classification 🧮 math.ST stat.TH
keywords concentrationreplacementsamplingwithoutboundinequalitiesinequalityknown
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Concentration inequalities quantify the deviation of a random variable from a fixed value. In spite of numerous applications, such as opinion surveys or ecological counting procedures, few concentration results are known for the setting of sampling without replacement from a finite population. Until now, the best general concentration inequality has been a Hoeffding inequality due to Serfling [Ann. Statist. 2 (1974) 39-48]. In this paper, we first improve on the fundamental result of Serfling [Ann. Statist. 2 (1974) 39-48], and further extend it to obtain a Bernstein concentration bound for sampling without replacement. We then derive an empirical version of our bound that does not require the variance to be known to the user.

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