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Journal Articles Bernoulli Year : 2015

Concentration inequalities for sampling without replacement

Abstract

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 ?. In this paper, we first improve on the fundamental result of ?, 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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Dates and versions

hal-01216652 , version 1 (16-10-2015)

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Rémi Bardenet, Odalric-Ambrym Maillard. Concentration inequalities for sampling without replacement. Bernoulli, 2015, 21 (3), pp.1361-1385. ⟨10.3150/14-BEJ605⟩. ⟨hal-01216652⟩
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