On Stein's method for multivariate normal approximation
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Publication:2900954
DOI10.1214/09-IMSCOLL511zbMATH Open1243.60025arXiv0902.0333OpenAlexW1531920432MaRDI QIDQ2900954
Author name not available (Why is that?)
Publication date: 26 July 2012
Published in: (Search for Journal in Brave)
Abstract: 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.
Full work available at URL: https://arxiv.org/abs/0902.0333
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