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arXiv · 1903.09319

Stein's method via induction

Louis H. Y. Chen·Larry Goldstein·Adrian Röllin
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Abstract

Applying an inductive technique for Stein and zero bias couplings yields Berry-Esseen theorems for normal approximation 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, and can produce bounds in the Kolmogorov metric with the optimal rate.

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Louis H. Y. Chen, Larry Goldstein, Adrian Röllin. 2019-03-22. Stein's method via induction. https://arxiv.org/abs/1903.09319

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