Abstract
Normal approximation or, more generally the asymptotic theory, plays a fundamental role in the developments of modern probability and statistics. The one-dimensional central limit theorem and the Edgeworth expansion for independent real-valued random variables are well studied. We refer to the classical book by Petrov (1995). In the context of the multi-dimensional central limit theorem, Rabi Bhattacharya has made fundamental contributions to asymptotic expansions. The book by Bhattacharya and Ranga Rao (1976) is a standard reference. In this note I shall focus on two of his seminal papers (1975, 1977) on asymptotic expansions. Recent developments on normal approximation by Stein’s method and strong Gaussian approximation will also be discussed.
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Acknowledgements
The author would like to thank Xiao Fang, Weidong Liu, and Wenxin Zhou for their help in preparing this note. Partially supported by Hong Kong RGC - GRF 403513.
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Shao, QM. (2016). An Introduction to Normal Approximation. In: Denker, M., Waymire, E. (eds) Rabi N. Bhattacharya. Contemporary Mathematicians. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-30190-7_3
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DOI: https://doi.org/10.1007/978-3-319-30190-7_3
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