A Sharper Hoeffding Bound for Weighted Sums of Exchangeable Random Variables

Abstract

We prove a Hoeffding-type moment generating function bound for weighted sums of bounded exchangeable random variables centered by their finite-population average. The bound improves the finite-population inflation factor in a recent weighted exchangeable Hoeffding inequality from logarithmic order to the rate-optimal inverse-population-size order, with an explicit constant. The proof reduces the problem to Hamming slices, identifies two-level extremizers for the relevant symmetric variational problem, and applies a hypergeometric martingale bound. We also give a lower bound showing that an inverse-population-size inflation is unavoidable.