Normal Approximation by Stein's Method

By Louis H. Y. Chen, Larry Goldstein, Qi-Man Shao. 2010

259 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/c293a1173d040a36b6f44c3669876b743d1cae76

How researchers see this paper

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

In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

In Statistics and Probability

Citations in the corpus

Stein's method for steady-state diffusion approximations of $M/Ph/n+M$ systems (2015, methodology): “d 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 diﬀusion processes was ﬁrs”
Newton-Stein Method: An Optimization Method for GLMs via Stein's Lemma (2015, unknown): “Examples include Total Variation (TV), Kolmogorov and Wasserstein metrics (Gibbs and Su, 2002; Chen et al., 2010).”
Normal approximation by Stein’s method under sublinear expectations (2017, methodology): “The cornerstone of Stein’s method is the Stein equation (refer to [1] for more details): For a standard normally distributed random variable Z and given φ, solve the following equation for f , f ′(x)− xf(x) = φ(x) − E[φ(Z)].”
Approximation of stable law in Wasserstein-1 distance by Stein’s method (2017, methodology): “he details of this example in the appendix. Let us now roughly explain the strategy of our approaching. In normal approximations, one approach to Stein’s method introduced by Chen, Goldstein and Shao [15] is to write E[Snf(Sn)] = Xn i=1 Z∞ −∞ (1.1) E[Ki(t)f′(Sn(i)+t)]dt, where Sn(i) = Sn −ζn,i and K”
Stein's method for comparison of univariate distributions (2014, methodology): “ full freedom of choice provided by Theorem 44, but rather focus on applications of identity (59) only. Indeed in this case much is known about kghk and kDghk in case f 1 = 1 and X 1 is Gaussian (see [22]), Binomial (see [29]), Poisson (see [8]), Gamma (see [17, 66]), etc. See also [28, 54, 26, 61] ”
Heavy traffic approximation for the stationary distribution of a generalized Jackson network: The BAR approach (2015, methodology): “ead relied on the existence of Lyapunov functions for the diﬀusion approximation. Inspired by Gurvich’s work, Braverman and Dai [5] connect the ideas in [17] to Stein’s method [33] (see also [30] and [8]), and prove steady-state approximation error bounds in the case where service times follow a gen”
Stein’s density approach and information inequalities (2012, background): “ctions for lower half-lines (see [27, Theorem 3.4.2]); and (iii) κp p H ≤ π/2supl∈H min(kl−Ep [l(X)]k ∞,2kl′k ) for H the class of absolutely continuous functions on R (see [12, Lemma 2.3]). See also [3, 11, 27, 29] for more examples. Bounds such as (4.1) are sometimes too rough to be satisfactory. ”
Stein's method for steady-state diffusion approximations: an introduction through the Erlang-A and Erlang-C models (2015, methodology): “od 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 [5, 14], the recent book [6] and the references within. Barbour [2] has used Stein’s method to establish convergence rates fo”