A short survey of Stein's method

By Sourav Chatterjee. 2014

87 citations recorded by the source corpus.

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.

Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/829b39cbed85cac32bdd0d74ca6baaec58ea65b7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Discrete Mathematics and Combinatorics

In Geometry and Topology

In Statistics and Probability

Citations in the corpus

Stein's method for steady-state diffusion approximations of $M/Ph/n+M$ systems (2015, methodology): “n isolation. Stein’s method is a powerful method that has been widely used in probability, statistics, and their wide range of applications such as bioinformatics; see, for example, the survey papers [11, 45], the recent book [12] and the references within. The connection between Stein’s method and ”
Stein's method for comparison of univariate distributions (2014, background): “Also there exist many ways by which one can evaluate E [Af(W )] or E[AW f(W ) − AZf(W )] (even under unfavorable assumptions on W ) including exchangeable pairs (as for example in [91, 52, 85, 21, 19, 28]), biasing mechanisms (as in [4, 44, 41, 79, 37]), and other couplings (as in [22, 9]); see [84,”
Adjacency matrices of random digraphs: singularity and anti-concentration (2015, methodology): “The proof in [9] is based on the method of exchangeable pairs introduced by Stein and developed for concentration inequalities by Chatterjee (see survey [7] for more information and references).”
Stein's method for steady-state diffusion approximations: an introduction through the Erlang-A and Erlang-C models (2015, background): “It has been widely used in probability, statistics, and their wide range of applications such as bioinformatics; see, for example, the survey papers [52, 13], the recent book [15] and the references within.”
Universality and Sharp Matrix Concentration Inequalities (2022, methodology): “As will be explained in section 3, it appears that standard methods for proving universality, such as the Lindeberg and Stein methods [11], cannot adequately capture noncommutativity of the summands in (1.”