Concentration inequalities for sampling without replacement - Archive ouverte HAL Access content directly
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.
Fichier principal
Vignette du fichier
submittedArxiv.pdf (490.44 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

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

Identifiers

Cite

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

Altmetric

Share

Gmail Facebook Twitter LinkedIn More