# Stein's method for normal approximation

@inproceedings{Chen2005SteinsMF, title={Stein's method for normal approximation}, author={Louis H. Y. Chen and Qi-Man Shao}, year={2005} }

Stein’s method originated in 1972 in a paper in the Proceedings of the Sixth Berkeley Symposium. In that paper, he introduced the method in order to determine the accuracy of the normal approximation to the distribution of a sum of dependent random variables satisfying a mixing condition. Since then, many developments have taken place, both in extending the method beyond normal approximation and in applying the method to problems in other areas. In these lecture notes, we focus on univariate…

## 128 Citations

### On Stein's method and perturbations

- Mathematics
- 2007

Stein's (1972) method is a very general tool for assessing the quality of approximation of the distribution of a random element by another, often sim- pler, distribution. In applications of Stein's…

### eb 2 00 7 On Stein ’ s method and perturbations

- Mathematics
- 2007

Stein’s (1972) method is a very general tool for assessing the quality of approximation of the distribution of a random element by another, often simpler, distribution. In applications of Stein’s…

### New error bounds for Laplace approximation via Stein’s method

- Mathematics, Computer ScienceESAIM: Probability and Statistics
- 2021

We use Stein’s method to obtain explicit bounds on the rate of convergence for the Laplace approximation of two different sums of independent random variables; one being a random sum of mean zero…

### Gaussian approximation of functionals: Malliavin calculus and Stein’s method

- Mathematics
- 2011

Combining Malliavin calculus and Stein’s method has recently lead to a new framework for normal and for chi-square approximation, and for second-order Poincaré inequalities. Applications include…

### Multi-dimensional "Malliavin-Stein" method on the Poisson space and its applications to limit theorems

- Mathematics
- 2011

In this dissertation we focus on limit theorems and probabilistic approximations. A ''limit theorem'' is a result stating that the large-scale structure of some random system can be meaningfully…

### Stein's Method and Stochastic Analysis of Rademacher Functionals

- Mathematics, Computer Science
- 2008

Three main applications are provided: to CLTs for multilinear forms belonging to a fixed chaos, to the Gaussian approximation of weighted infinite 2-runs, and to the computation of explicit bounds inCLTs for multiple integrals over sparse sets.

### A simplified second-order Gaussian Poincar\'e inequality in discrete setting with applications

- Mathematics, Computer Science
- 2021

A simpli ed second-order Gaussian Poincaré inequality for normal approximation of functionals over in nitely many Rademacher random variables is derived and the number of vertices with prescribed degree and the subgraph counting statistic in the Erd®s-Rényi random graph are discussed.

### Stein's method of exchangeable pairs for the Beta distribution and generalizations

- Mathematics
- 2014

Abstract. We propose a version of Stein’s method of exchangeable pairs, which, given a suitable exchangeable pair (W,W ) of real-valued random variables, suggests the approximation of the law of W by…

### STEIN MEETS MALLIAVIN IN NORMAL APPROXIMATION

- Mathematics
- 2014

Stein’s method is a method of probability approximation which hinges on the solution of a functional equation. For normal approximation, the functional equation is a first-order differential…

### Stein couplings for normal approximation

- Mathematics
- 2010

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…

## References

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Abstract. This paper is part of our efforts to develop Stein's method beyond uniform bounds in normal approximation. Our main result is a proof for a non-uniform Berry–Esseen bound for independent…

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