Stein's method for normal approximation

  title={Stein's method for normal approximation},
  author={Louis H. Y. Chen and Qi-Man Shao},
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… 

On Stein's method and perturbations

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

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

  • Robert E. Gaunt
  • Mathematics, Computer Science
    ESAIM: 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

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

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

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

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

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Stein couplings for normal approximation

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Stein's method is used to obtain two theorems on multivariate normal approximation. Our main theorem, Theorem 1.2, provides a bound on the distance to normality for any non-negative random vector.

Stein's Method: Expository Lectures and Applications

A review of Stein’s method applied to the case of discrete random variables and attempt to complete one of Stein's open problems, that of providing a discrete version for chapter 6 of his book.

A bound for the error in the normal approximation to the distribution of a sum of dependent random variables

This paper has two aims, one fairly concrete and the other more abstract. In Section 3, bounds are obtained under certain conditions for the departure of the distribution of the sum of n terms of a

Probability Theory, an Analytic View

This second edition of Daniel W. Stroock's text is suitable for first-year graduate students with a good grasp of introductory, undergraduate probability theory and a sound grounding in analysis. It

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Abstract.Stein's method for normal approximations is explained, with some examples and applications. In the study of the asymptotic distribution of the sum of dependent random variables, Stein's

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The Rate of Convergence for Multivariate Sampling Statistics

A Berry-Esseen theorem for the rate of convergence of general nonlinear multivariate sampling statistics with normal limit distribution is derived via a multivariate extension of Stein's method. The