Fundamentals of Stein's method

@article{Ross2011FundamentalsOS,
  title={Fundamentals of Stein's method},
  author={Nathan Ross},
  journal={Probability Surveys},
  year={2011},
  volume={8},
  pages={210-293}
}
  • Nathan Ross
  • Published 9 September 2011
  • Mathematics
  • Probability Surveys
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 relation to concentration of measure inequalities. The material is presented at a level accessible to beginning raduate students studying probability with the main emphasis on the themes that are common to these topics and also to much of the Stein's method literature. 
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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.
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The aim of this paper is to give an overview of Stein’s method, which has turned out to be a powerful tool for estimating the error in normal, Poisson and other approximations, especially for sums of
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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
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A common theme in probability theory is the approximation of complicated probability distributions by simpler ones, the central limit theorem being a classical example. Stein's method is a tool which
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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
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