Stein's method via induction

Louis H. Y. Chen, Larry Goldstein, Adrian Röllin

Published 2019-03-22Version 1

Applying an inductive technique for Stein and zero bias couplings yields Berry-Esseen theorems for normal approximation with optimal rates in the Kolmogorov metric for two new examples. The conditions of the main results do not require that the couplings be bounded. Our two applications, one to the Erd\H{o}s-R\'enyi random graph with a fixed number of edges, and one to Jack measure on tableaux, demonstrate that the method can handle non-bounded variables with non-trivial global dependence.