Multivariate Concentration Inequalities with Size Biased Couplings

Abstract

Let $\mathbf{W}=(W_1,W_2,...,W_k)$ be a random vector with nonnegative coordinates having nonzero and finite variances. We prove concentration inequalities for $\mathbf{W}$ using size biased couplings that generalize the previous univariate results. Two applications on local dependence and counting patterns are provided.

arXiv comment10 pages

References in corpus (1)

• Bounded size bias coupling: a Gamma function bound, and universal Dickman-function behavior

Cited by in corpus (1)

• Bounded size bias coupling: a Gamma function bound, and universal Dickman-function behavior