A non-uniform Berry–Esseen bound via Stein's method

By Louis H. Y. Chen, Qi-Man Shao. 2001

146 citations recorded by the source corpus.

Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/7a4b31ba07efedc74b1289490515b420df95df0d

How researchers see this paper

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

In Applied Mathematics

In Discrete Mathematics and Combinatorics

In Statistics and Probability

Citations in the corpus

Stein's method for normal approximation (2005, methodology): “The approach has further been shown to be effective in obtaining not only uniform but also non-uniform Berry–Esseen bounds for the accuracy of normal approximation for independent random variables (Chen & Shao, 2001) and for locally dependent random fields as well (Chen & Shao, 2004a).”
A multivariate Berry–Esseen theorem with explicit constants (2018, methodology): “This is much worse than K = 4.1 obtained by Chen and Shao [11] by Stein’s method, let alone than K = 0.5583 obtained by Shevtsova [24] by Fourier methods.”
Stein couplings for normal approximation (2010, background): “Note that, here and in later results, the truncation constant 1 is not chosen arbitrarily as the truncation at 1 has some optimality properties; see Loh (1975) and Chen and Shao (2001).”
IMPROVEMENT OF THE NON-UNIFORM VERSION OF BERRY-ESSEEN INEQUALITY VIA PADITZ-SIGANOV THEOREMS (2007, background): “In 2001, Chen and Shao ([3]) gave new versions of (1.1) and (1.2) without assuming the existence of third moments.”
A Multivariate CLT for Decomposable Random Vectors with Finite Second Moments (2004, background): “(23) The following variant of Katz’s result was proved by Chen and Shao ( 14 ) (see”
Normal approximation under local dependence (2004, methodology): “Whenx > 6, the proof of (5.22) is very similar to that of Lemma 5.2 of Chen and Shao (2001).”
Normal approximation for nonlinear statistics using a concentration inequality approach (2007, methodology): “The research of L.H.Y. Chen was partially supported by National University of Singapore grant R-146-000-013-112, and the research of Q.M. Shao was partially supported by NSF grant DMS-0103487, National University of Singapore grant R-146-000-038-101 and HKUST grant DAG 05/06.”