Concentration inequalities for sampling without replacement.

Rémi Bardenet, Odalric-Ambrym Maillard.
In Bernoulli Journal, 2014.

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 Serfling (1974). In this paper, we first improve on the fundamental result of Serfling (1974), 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.

You can dowload the paper from the Bernoulli website (here) or from the HAL online open depository* (here).

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* The HAL open-access online archive system seeks to make research results available to the widest audience, independently of the major publisher, and cooperates with other large international archives like arXiv.

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