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A non-uniform Berry–Esseen bound via Stein's method
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  • Published: June 2001

A non-uniform Berry–Esseen bound via Stein's method

  • Louis H.Y. Chen1 &
  • Qi-Man Shao2 

Probability Theory and Related Fields volume 120, pages 236–254 (2001)Cite this article

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Abstract.

This paper is part of our efforts to develop Stein's method beyond uniform bounds in normal approximation. Our main result is a proof for a non-uniform Berry–Esseen bound for independent and not necessarily identically distributed random variables without assuming the existence of third moments. It is proved by combining truncation with Stein's method and by taking the concentration inequality approach, improved and adapted for non-uniform bounds. To illustrate the technique, we give a proof for a uniform Berry–Esseen bound without assuming the existence of third moments.

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543, Republic of Singapore. e-mail: lhychen@math.nus.edu.sg, , , , , , SG

    Louis H.Y. Chen

  2. Department of Mathematics, University of Oregon, Eugene, OR 97403, USA. e-mail: shao@math.uoregon.edu, , , , , , US

    Qi-Man Shao

Authors
  1. Louis H.Y. Chen
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  2. Qi-Man Shao
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Received: 2 March 2000 / Revised version: 20 July 2000 / Published online: 26 April 2001

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Chen, L., Shao, QM. A non-uniform Berry–Esseen bound via Stein's method. Probab Theory Relat Fields 120, 236–254 (2001). https://doi.org/10.1007/PL00008782

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  • Issue Date: June 2001

  • DOI: https://doi.org/10.1007/PL00008782

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  • Mathematics Subject Classification (2000): Primary 60F05; Secondary 60G50
  • Key words or phrases: Stein's method – Normal approximation – Non-uniform Berry–Esseen bound – Concentration inequality approach
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