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Probability Approximations and Beyond pp 13–30Cite as

Berry-Esseen Inequality for Unbounded Exchangeable Pairs

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Part of the book series: Lecture Notes in Statistics ((LNSP,volume 205))

Abstract

The Berry-Esseen inequality is well-established by the Stein method of exchangeable pair approach when the difference of the pair is bounded. In this paper we obtain a general result which can achieve the optimal bound under some moment assumptions. As an application, a Berry-Esseen bound of \(O(1/\sqrt{n})\) is derived for an independence test based on the sum of squared sample correlation coefficients.

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Acknowledgments

The second author is partially supported by Hong Kong RGC CERG 602608 and 603710.

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Authors and Affiliations

  1. Department of Mathematics, Hong Kong University of Science and Technology, Kowloon, Clear Water Bay, Hong Kong, China

    Yanchu Chen & Qi-Man Shao

Authors
  1. Yanchu Chen
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  2. Qi-Man Shao
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Corresponding author

Correspondence to Yanchu Chen .

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Editors and Affiliations

  1. Institut für Mathematik, Universität Zürich, Winterthurerstr. 190, Zürich, 8057, Switzerland

    Andrew Barbour

  2. , Department of Statistics and Applied Pro, National University of Singapore, Singapore, 119260, Singapore

    Hock Peng Chan

  3. Dept. Statistics, Stanford University, Serra Mall 390, Stanford, 94305, California, USA

    David Siegmund

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Chen, Y., Shao, QM. (2012). Berry-Esseen Inequality for Unbounded Exchangeable Pairs. In: Barbour, A., Chan, H., Siegmund, D. (eds) Probability Approximations and Beyond. Lecture Notes in Statistics(), vol 205. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-1966-2_2

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