Berry-Esseen Inequality for Unbounded Exchangeable Pairs

  • Yanchu ChenEmail author
  • Qi-Man Shao
Conference paper
Part of the Lecture Notes in Statistics book series (LNS, volume 205)


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.


Asymptotic Theory Multivariate Normal Distribution Sample Correlation Independence Test Likelihood Ratio Test Statistic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



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


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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Department of MathematicsHong Kong University of Science and TechnologyKowloon, Clear Water BayChina

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