A short survey of Stein's method

Abstract

Stein's method is a powerful technique for proving central limit theorems in probability theory when more straightforward approaches cannot be implemented easily. This article begins with a survey of the historical development of Stein's method and some recent advances. This is followed by a description of a "general purpose" variant of Stein's method that may be called the generalized perturbative approach, and an application of this method to minimal spanning trees. The article concludes with the descriptions of some well known open problems that may possibly be solved by the perturbative approach or some other variant of Stein's method.

Contribution to the Proceedings of the ICM 2014. 25 pages

References in corpus (5)

• Normal approximation under local dependence
• A new method of normal approximation
• Exponential Approximation by Stein's Method and Spectral Graph Theory
• A note on the exchangeability condition in Stein's method
• An Exposition of Götze's Estimation of the Rate of Convergence in the Multivariate Central Limit Theorem

Cited by in corpus (5)

• Approximation of Riemannian measures by Stein's method
• Stein's method for dynamical systems
• A quantitative central limit theorem for the effective conductance on the discrete torus
• Constructing exchangeable pairs by diffusion on manifolds and its application
• Stability estimates for invariant measures of diffusion processes, with applications to stability of moment measures and Stein kernels