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Normal approximations by Stein's method

Author

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  • Yosef Rinott
  • Vladimir Rotar

Abstract

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, 2014. "Central limit theorems and bootstrap in high dimensions," CeMMAP working papers CWP49/14, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    2. Victor Chernozhukov & Denis Chetverikov & Kengo Kato, 2012. "Gaussian approximations and multiplier bootstrap for maxima of sums of high-dimensional random vectors," Papers 1212.6906, arXiv.org, revised Jan 2018.
    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. Rinott, Yosef & Scarsini, Marco, 2000. "On the Number of Pure Strategy Nash Equilibria in Random Games," Games and Economic Behavior, Elsevier, vol. 33(2), pages 274-293, November.
    5. Christophe Ley & Gesine Reinert & Yvik Swan, 2014. "Approximate Computation of Expectations: the Canonical Stein Operator," Working Papers ECARES ECARES 2014-36, ULB -- Universite Libre de Bruxelles.
    6. Kasprzak, Mikołaj J., 2020. "Stein’s method for multivariate Brownian approximations of sums under dependence," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4927-4967.
    7. Ghosh, Subhankar & Goldstein, Larry & Raic, Martin, 2011. "Concentration of measure for the number of isolated vertices in the Erdos-Rényi random graph by size bias couplings," Statistics & Probability Letters, Elsevier, vol. 81(11), pages 1565-1570, November.
    8. Lina Zhang, 2020. "Spillovers of Program Benefits with Missing Network Links," Papers 2009.09614, arXiv.org, revised Apr 2023.
    9. James C. Fu & W. Y. Wendy Lou, 2007. "On the Normal Approximation for the Distribution of the Number of Simple or Compound Patterns in a Random Sequence of Multi-state Trials," Methodology and Computing in Applied Probability, Springer, vol. 9(2), pages 195-205, June.
    10. Christophe Ley & Yvik Swan, 2011. "A unified approach to Stein characterizations," Working Papers ECARES 2013/88988, ULB -- Universite Libre de Bruxelles.

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