Open Access
August 2015 Concentration inequalities for sampling without replacement
Rémi Bardenet, Odalric-Ambrym Maillard
Bernoulli 21(3): 1361-1385 (August 2015). DOI: 10.3150/14-BEJ605


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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Rémi Bardenet. Odalric-Ambrym Maillard. "Concentration inequalities for sampling without replacement." Bernoulli 21 (3) 1361 - 1385, August 2015.


Received: 1 September 2013; Revised: 1 January 2014; Published: August 2015
First available in Project Euclid: 27 May 2015

zbMATH: 06470443
MathSciNet: MR3352047
Digital Object Identifier: 10.3150/14-BEJ605

Keywords: Bernstein , Concentration bounds , sampling without replacement , Serfling

Rights: Copyright © 2015 Bernoulli Society for Mathematical Statistics and Probability

Vol.21 • No. 3 • August 2015
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