An Introduction to Stein's Method

By A. Barbour, Louis H. Y. Chen. 2005

243 citations recorded by the source corpus.

Subfields: Clinical Psychology, Cognitive Neuroscience, Developmental and Educational Psychology

View Paper: https://www.semanticscholar.org/paper/5388df1800919c9dd793082536e66dc9d9a51ad0

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In Clinical Psychology

In Cognitive Neuroscience

In Developmental and Educational Psychology

Citations in the corpus

Estimating the unseen: an n/log(n)-sample estimator for entropy and support size, shown optimal via new CLTs (2011, background): “1 provides a simple illustration of Theorem 3, in the univariate setting (k = 1); of course, in the univariate setting, such central limit theorems are standard (see [5]).”
Stein’s density approach and information inequalities (2012, background): “For the origins we refer the reader to [39, 37, 36]; for an overview of the more recent achievements in this field we refer to the monographs [27, 3, 11] or the review articles [26, 30].”
Stein's method for comparison of univariate distributions (2014, unknown): “, [6, 8]).”
Optimal-order bounds on the rate of convergence to normality in the multivariate delta method (2009, unknown): “1057 F On the spectral decomposition of a covariance operator of a random vector in an arbitrary separable Hilbert space . . . . . . . . . . . . . 1057 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1058”
A short survey of Stein's method (2014, background): “The edited volumes [9] and [40] are also worth a look.”
Action-depedent Control Variates for Policy Optimization via Stein's Identity (2017, background): “…function φ(s, a), which is sufficient to uniquely identify a distribution as shown in the work of Stein’s method for proving central limit theorems (Stein, 1986; Barbour & Chen, 2005), goodness-of-fit test (Chwialkowski et al., 2016; Liu et al., 2016), and approximate inference (Liu & Wang, 2016).”
Fundamentals of Stein's method (2011, methodology): “There are numerous other introductions to Stein’s method which this document draws from, mainly [23, 24] for Normal approximation, [12, 20] for Poisson approximation, and an amalgamation of related topics in the collections [11, 26].”
On integral probability metrics, φ-divergences and binary classification (2009, background): “…φ -divergences, and especially the KL-divergence, are better known and more widely used in diverse ﬁelds such as neuro-science [10]–[12] and distribution testing [13]–[16], however they are notoriously tough to estimate, especially in high dimensions, d , when M = R d , e.g., see [17].”
Exponential Approximation by Stein's Method and Spectral Graph Theory (2006, methodology): “We hope that this approach will be useful in other settings (a concentration inequality for W ′ − W can be very useful for normal approximation by Stein’s method; see the survey Chen and Shao, 2005).”
From Stein identities to moderate deviations (2009, unknown): “Expositions of Stein’s method and its applications in normal and other distributional approximations can be found in Diaconis and Holmes (2004) and Barbour and Chen (2005).”
Hilbert Space Embeddings and Metrics on Probability Measures (2009, methodology): “In addition to the general application domains discussed earlier for metrics on probabilities, IPMs have been used in proving central limit theorems using Stein’s method (Stein, 1972; Barbour and Chen, 2005), and are popular in empirical process theory (van der Vaart and Wellner, 1996).”
Entry and return times distribution (2013, background): “then has for every ν0-integrable h ∈ F a solution f that is unique except for f(0), which can be chosen arbitrarily [47]1.”