# 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} }

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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