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2020 Stein’s method via induction
Louis H.Y. Chen, Larry Goldstein, Adrian Röllin
Electron. J. Probab. 25: 1-49 (2020). DOI: 10.1214/20-EJP535

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 Erdős-Rényi 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. "Stein’s method via induction." Electron. J. Probab. 25 1 - 49, 2020. https://doi.org/10.1214/20-EJP535

Information

Received: 22 March 2019; Accepted: 4 October 2020; Published: 2020
First available in Project Euclid: 28 October 2020

MathSciNet: MR4169173
Digital Object Identifier: 10.1214/20-EJP535

Subjects:
Primary: 60F05
Secondary: 05C07, 05C80, 05E10

JOURNAL ARTICLE
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