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Normal approximations by Stein's method


  • Yosef Rinott
  • Vladimir Rotar


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 method may be a very useful tool. We have attempted to write an elementary introduction. For more advanced introductions to Stein's method, see Stein (1986), Barbour (1997) and Chen (1998).

Suggested Citation

  • Yosef Rinott & Vladimir Rotar, 2000. "Normal approximations by Stein's method," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 23(1), pages 15-29.
  • Handle: RePEc:spr:decfin:v:23:y:2000:i:1:p:15-29
    Note: Received: 6 December 1999

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    Cited by:

    1. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors," Papers 1212.6906,, revised Jan 2018.
    2. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2014. "Central limit theorems and bootstrap in high dimensions," CeMMAP working papers CWP49/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Zhichao Zheng & Karthik Natarajan & Chung-Piaw Teo, 2016. "Least Squares Approximation to the Distribution of Project Completion Times with Gaussian Uncertainty," Operations Research, INFORMS, vol. 64(6), pages 1406-1421, December.
    4. Christophe Ley & Gesine Reinert & Yves-Caoimhin Swan, 2014. "Approximate Computation of Expectations: the Canonical Stein Operator," Working Papers ECARES ECARES 2014-36, ULB -- Universite Libre de Bruxelles.
    5. Christophe Ley & Yves-Caoimhin Swan, 2011. "A unified approach to Stein characterizations," Working Papers ECARES 2013/88988, ULB -- Universite Libre de Bruxelles.
    6. Yun-Xia Li & Jian-Feng Wang, 2008. "An application of Stein’s method to limit theorems for pairwise negative quadrant dependent random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(1), pages 1-10, January.

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