A bound for the error in the normal approximation to the distribution of a sum of dependent random variables

By C. Stein. 1972

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Citations in the corpus

A Kernelized Stein Discrepancy for Goodness-of-fit Tests (2016, methodology): “Stein’s method (Stein, 1972) is a general theoretical tool for obtaining bounds on distances between distributions.”
A Kernel Test of Goodness of Fit (2016, background): “Similarly to Stein (1972); Gorham & Mackey (2015); Oates et al. (2016), we begin by defining a Stein operator Tp acting on f ∈ Fd (Tpf)(x) := d∑ i=1 ( ∂ log p(x) ∂xi fi(x) + ∂fi(x) ∂xi ) .”
Control functionals for Monte Carlo integration (2014, background): “Equation (1) appears in Stein’s classical test for approximate normality (Stein, 1970) and related to (but simpler than) control variates proposed by Assaraf and Caffarel (1999) and Mira et al. (2013).”
Hilbert Space Embeddings and Metrics on Probability Measures (2009, background): “It is to be noted that when M is compact, this notion of universality is same as that of Steinwart (2001). Mic chelli et al.”
On integral probability metrics, φ-divergences and binary classification (2009, methodology): “In probability theory, IPMs a re used in proving central limit theorems using Stein’s method [18], [19].”
Learning to Draw Samples: With Application to Amortized MLE for Generative Adversarial Learning (2016, methodology): “Stein variational gradient descent (SVGD) (Liu & Wang, 2016) is a general purpose Bayesian inference algorithm motivated by Stein’s method (Stein, 1972; Barbour & Chen, 2005) and kernelized Stein discrepancy (Liu et al., 2016; Chwialkowski et al., 2016; Oates et al., 2014).”
Basic properties of strong mixing conditions. A survey and some open questions (2005, neutral): “Random elds”
Score Function Features for Discriminative Learning: Matrix and Tensor Framework (2014, background): “l version of Stein’s lemma is for the Gaussian distribution. For a standard random Gaussian vector x ∼ N(0,Idx), it states that for all functions7 G(x) satisfying mild regularity conditions, we have (Stein, 1972) E[G(x) ⊗x] = E[∇xG(x)], (5) where ⊗ denotes the tensor product (note that if G(x) is a ”
Robust generalised Bayesian inference for intractable likelihoods (2021, unknown): “The approach is based on the method of Stein (1972), which requires the identification of a linear operator  Q ∶  → L 1 (  , Q ) , depending on a probability distribution Q ∈  (  ) and acting on a Banach space  , such that Such an operator  Q is called a Stein operator and  is called a…”
Use of exchangeable pairs in the analysis of simulations (2004, background): “As in Stein [27], Chapter 6, we first derive a characterization for a continuous distribution.”
Chi-square approximation by Stein's method with application to Pearson's statistic (2015, methodology): “Stein’s method was introduced in [32] for assessing the distance between a probability distribution and the normal distribution.”
Normal Approximation by Stein's Method (2010, unknown): “Problems 12 • Stein86 =Stein (1986) • Stein72 = Stein (1972).”
A NEW METHOD OF NORMAL APPROXIMATION (2006, methodology): “This is the key idea behind Stein’s method of normal approximation, introduced by Charles Stein in the seminal paper [40] and later developed in his book [41].”
Matrix concentration inequalities via the method of exchangeable pairs (2012, methodology): “Our approach to studying random matrices is based on the method of exchangeable pairs, which originates in the work of Charles Stein [47] on normal approximation for a sum of dependent random variables.”