Rémi Bardenet, Odalric-Ambrym Maillard.
In Bernoulli Journal, 2014.
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| Abstract: |
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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 (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. |
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| Bibtex: |
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Odalric-Ambrym Maillard 