Stein couplings for normal approximation

By Louis H. Y. Chen, Adrian Röllin. 2010

55 citations recorded by the source corpus.

In this article we propose a general framework for normal approximation using Stein's method. We introduce the new concept of Stein couplings and we show that it lies at the heart of popular approaches such as the local approach, exchangeable pairs, size biasing and many other approaches. We prove several theorems with which normal approximation for the Wasserstein and Kolmogorov metrics becomes routine once a Stein coupling is found. To illustrate the versatility of our framework we give applications in Hoeffding's combinatorial central limit theorem, functionals in the classic occupancy scheme, neighbourhood statistics of point patterns with fixed number of points and functionals of the components of randomly chosen vertices of sub-critical Erdos-Renyi random graphs. In all these cases, we use new, non-standard couplings.

Subfields: Discrete Mathematics and Combinatorics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/04ca160f55839e310137d51c266022bb3f8c67f4

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Citations in the corpus

Fundamentals of Stein's method (2011, background): “We will identify general structures that are amenable to this task (for other structures in greater generality see [46]), but first we illustrate the type of result we are looking for in the following standard example.”
New rates for exponential approximation and the theorems of Rényi and Yaglom (2011, methodology): “Our second approach involves an adaptation of the linear Stein couplings intro duced in Chen and Rollin (2009).”
From Stein identities to moderate deviations (2009, unknown): “For normal approximation there are four methods for constructing a Stein identity: the direct method (Stein (1972)), zero-bias coupling (Goldstein and Reinert (1997) and Goldstein (2005)), exchangeable pairs (Stein (1986)), and Stein coupling (Chen and Röllin (2010)).”
A short survey of Stein's method (2014, methodology): “Further advances were made in the recent manuscript of Röllin [75].”
High-dimensional central limit theorems by Stein’s method (2020, methodology): “Next, we consider nonlinear statistics along the lines of Chatterjee (2008a), Chen and Röllin (2010) and Dung (2019).”