On normal approximation rates for certain sums of dependent random variables

@article{Rinott1994OnNA,
  title={On normal approximation rates for certain sums of dependent random variables},
  author={Yosef Rinott},
  journal={Journal of Computational and Applied Mathematics},
  year={1994},
  volume={55},
  pages={135-143}
}
  • Y. Rinott
  • Published 21 November 1994
  • Mathematics
  • Journal of Computational and Applied Mathematics
Abstract Let X1, …, Xn be dependent random variables, and set λ = E∑ni=1Xi, and σ2 = Var∑ni=1Xi. In most of the applications of Stein's method for normal approximations, the error rate |P((∑ni=1Xi − λ)/σ ⩽ w) − Φ(w)| is of the order of σ− 1 2 . This rate was improved by Stein (1986) and others in some special cases. In this paper it is shown that for certain bounded random variables, a simple refinement of error-term calculations in Stein's method leads to improved rates. 
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Stein's method of obtaining rates of convergence to the normal distribution is illustrated in the context of random graph theory and results are obtained for the number of copies of a given graph G in K. Expand
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