Stein's Method: A New Perspective on Normal and Non-normal Approximation

The classical proof of the central limit theorem is based on the characteristic function or the Fourier transform. It works well for sums of independent 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 the fundamentals of Stein's method and recent developments in this area.