Hoeffding and Bernstein inequalities for weighted sums of exchangeable random variables

Abstract: The aim of this paper is to establish Hoeffding and Bernstein type concentration inequalities for weighted sums of exchangeable random variables. A special case is the i.i.d. setting, where random variables are sampled independently from some distribution (and are therefore exchangeable). In contrast to the existing literature on this problem, our results provide a natural unified view of both the i.i.d. and the exchangeable setting.