• Corpus ID: 118347930

A short survey of Stein's method

@article{Chatterjee2014ASS,
  title={A short survey of Stein's method},
  author={Sourav Chatterjee},
  journal={arXiv: Probability},
  year={2014}
}
Stein's method is a powerful technique for proving central limit theorems in probability theory when more straightforward approaches cannot be implemented easily. This article begins with a survey of the historical development of Stein's method and some recent advances. This is followed by a description of a "general purpose" variant of Stein's method that may be called the generalized perturbative approach, and an application of this method to minimal spanning trees. The article concludes with… 
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64 Citations
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References

SHOWING 1-10 OF 88 REFERENCES
Stein's Method: Expository Lectures and Applications
TLDR
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.
Stein’s method for birth and death chains
This article presents a review of Stein's method applied to the case of discrete random variables. We attempt to complete one of Stein's open problems, that of providing a discrete version for…
Stein’s method for Markov chains: first examples
Charles Stein has introduced a general approach to proving approx- imation theorems in probability theory. The method is being actively used for normal and Poisson approximation. This paper uses the…
Fundamentals of Stein's method
This survey article discusses the main concepts and techniques of Stein's method for distributional approximation by the normal, Poisson, exponential, and geometric distributions, and also its…
A NEW METHOD OF NORMAL APPROXIMATION
We introduce a new version of Stein's method that reduces a large class of normal approximation problems to variance bounding exercises, thus making a connection between central limit theorems and…
An Exposition of Götze's Estimation of the Rate of Convergence in the Multivariate Central Limit Theorem
We provide an explanation of the main ideas underlying G\"otze's main result in using Stein's method. We also provide detailed derivations of various intermediate estimates. Curiously, we are led to…
Stein couplings for normal approximation
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…
Stein's method for diffusion approximations
SummaryStein's method of obtaining distributional approximations is developed in the context of functional approximation by the Wiener process and other Gaussian processes. An appropriate analogue of…
Stein's method for geometric approximation
The Stein–Chen method for Poisson approximation is adapted to the setting of the geometric distribution. This yields a convenient method for assessing the accuracy of the geometric approximation to…
Poisson Approximation and the Chen-Stein Method
The Chen-Stein method of Poisson approximation is a powerful tool for computing an error bound when approximating probabilities using the Poisson distribution. In many cases, this bound may be given…
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