Stein's method for normal approximation

By Louis H. Y. Chen, Qi-Man Shao. 2005

140 citations recorded by the source corpus.

Subfields: Discrete Mathematics and Combinatorics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d305626ef13ca557687965a9e24e89ead0ff1fea

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In Discrete Mathematics and Combinatorics

In Statistics and Probability

Citations in the corpus

Central limit theorems for $U$-statistics of Poisson point processes (2011, background): “ons h:R→Rwith a Lipschitz-constant less than or equal to one. It is important to note that convergence in the Wasserstein distance implies convergence in distribution. In particular, it is known (see [4], e.g.) that for a Gaussian random variable N we have |P(Y ≤t)−P(N ≤t)|≤2 p dW(Y,N) for all t∈R. ”
Stein's Method of Exchangeable Pairs with Application to the Curie-Weiss Model (2009, methodology): “We refer to Stein (1986), Rinott and Rotar (1997), Chen and Shao (2005) and references therein for the general theory of Stein’s method.”
From Stein identities to moderate deviations (2009, unknown): “Extensive applications of Stein’s method to obtain Berry–Esseen-type bounds for dependent random variables can be found in, for example, Diaconis (1977), Baldi, Rinott and Stein (1989), Barbour (1990), Dembo and Rinott (1996),”
Stein's method for dependent random variables occurring in Statistical Mechanics (2009, background): “2 in [5] or alternatively of Lemma 2 in [20, Lecture II] would lead to optimal constants.”
Stein's Method and Stochastic Analysis of Rademacher Functionals (2008, methodology): “The connection between Stein’s method (see e.g. [7, 33, 38, 39]) and the integration by parts formulae of stochastic analysis has been the object of a recent and quite fruitful study.”
A NEW METHOD OF NORMAL APPROXIMATION (2006, background): “are sharp. For a diﬀerent proof of the bound on kϕ′k∞, see Lemma 1 in [33]. The bound on kϕ′′k∞ is due to Stein ([41], page 27). Easier proofs with suboptimal constants can be found in Chen and Shao ([14], Chapter 1, Lemma 2.3). Proof of Lemma 4.2. It can be veriﬁed that the function ϕ(x) =ex2/2 Zx ”
Stein’s method on Wiener chaos (2007, background): “[11]), in order to obtain bounds analogous to (1.”
Cumulants on the Wiener Space (2009, methodology): “…important step appears in [13], where integration by parts on Wiener space is combined with the so-called Stein’s method for probabilistic approximations (see e.g. [6, 25]), thus yielding explicit upper bounds in the normal and gamma approximations of the law of functionals of Gaussian ﬁelds.”
Second order Poincaré inequalities and CLTs on Wiener space (2008, methodology): “A relation such as (1.4) is called a second order Poincar inequality: it is proved in [4] by combining (1.3) with an adequate version of Stein’s method (see e.g. [ 8 , 24]).”
Stein couplings for normal approximation (2010, methodology): “We call this the concentration inequality approach; see Ho and Chen (1978), Chen and Shao (2005), Shao and Su (2006), Chatterjee, Fulman, and Röllin (2006).”
Stein's method meets Malliavin calculus: a short survey with new estimates (2009, background): “In the last thirty years, an impressive panoply of approaches has been developed in this direction: the reader is referred to the two surveys by Chen and Shao [7] and Reinert [33] for a detailed discussion of these contributions.”
Asymptotic distribution-free change-point detection for multivariate and non-Euclidean data (2017, methodology): “Here, we look closer at the method in Chen and Zhang (2015). It is a scan statistic Z(t) calculated based on a graphbased two-sample test.”
Normal Approximation of Poisson Functionals in Kolmogorov Distance (2012, background): “For a detailed and more general introduction into this topic, we refer to [1,2,18].”