On Stein's method for multivariate normal approximation
By Elizabeth Meckes. 2009
104 citations recorded by the source corpus.
The purpose of this paper is to synthesize the approaches taken by Chatterjee-Meckes and Reinert-R\"ollin in adapting Stein's method of exchangeable pairs for multivariate normal approximation. The more general linear regression condition of Reinert-R\"ollin allows for wider applicability of the method, while the method of bounding the solution of the Stein equation due to Chatterjee-Meckes allows for improved convergence rates. Two abstract normal approximation theorems are proved, one for use when the underlying symmetries of the random variables are discrete, and one for use in contexts in which continuous symmetry groups are present. The application to runs on the line from Reinert-R\"ollin is reworked to demonstrate the improvement in convergence rates, and a new application to joint value distributions of eigenfunctions of the Laplace-Beltrami operator on a compact Riemannian manifold is presented.
Subfields: Applied Mathematics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/f31e06681342a50b4a7a4edd4524244acdbe522b
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In Applied Mathematics
- Louis H. Y. Chen
- Qi-Man Shao
- Jackson Gorham
- Lester W. Mackey
- Larry Goldstein
- Sandra Jeanne Vollmer
- Andrew B. Duncan
- Li-Xin Zhang
In Statistics and Probability
- Louis H. Y. Chen
- Qi-Man Shao
- Jackson Gorham
- Lester W. Mackey
- Larry Goldstein
- Sandra Jeanne Vollmer
- Andrew B. Duncan
- Sourav Chatterjee
Citations in the corpus
- Normal Approximation by Stein's Method (2010, background): “• BR76 = Bhattacharya and Ranga Rao (1976) • RR96 = Rinott and Rotar (1996) and RR97= Rinott and Rotar (1997) • MT = Meckes (2006) Ph.D. thesis • Alea = Chatterjee and Meckes (2008) • Luminy = Meckes (2009), Luminy paper • PTTM = Pollard (2029) and UGMTP = Pollard (2001).”
- Chi-square approximation by Stein's method with application to Pearson's statistic (2015, unknown): “15) is well-defined and is given by (see [24]): ψi(s) = − ∫ ∞”
- Measuring Sample Quality with Diffusions (2016, background): “11 Example 1 (Bayesian logistic regression with Gaussian prior).”