摘要：The characteristic function or the Fourier transform is a classical approach for distribution approximation. It works well for sums of independent random variables, but it may be very dicult to use for dependent random variables. The Stein method is a completely novel approach that works not only for independent random variables but also for dependent random variables. It works for both normal and non-normal approximation. It can also provide the accuracy of approximation. In this talk we will give a brief review on fundamentals of Stein's method and recent developments in this area. The connection between Stein's method and the Riemann hypothesis will also be discussed.

个人简介：Qi-Man Shao is currently Chair Professor at Southern University of Science and Technology, also Choh-Ming Li Professor of Statistics at the Chinese University of Hong Kong. His main research interests include asymptotic theory in probability and statistics, self-normalized limit theory, Stein’s method for normal and non-normal approximation, and high dimensional and large scale statistical analysis.

      He is an elected Fellow of the Institute of Mathematical Statistics (IMS), an invited speaker at the International Congress of Mathematicians (2010), IMS Medallion Lecturer (a keynote speaker) at the 2011 Joint Statistical Meetings. He was awarded the State Natural Science Award (2^nd class) in 2015.

      He was associate editor for Annals of Statistics and Annals of Applied Probability. He is currently an Associate Editor for Bernoulli, and an Associate Editor-in-chief for Science China: Mathematics.  

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