On Stein's method for multivariate normal approximation

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.

• Publication year

  2009

• Venue

  arXiv: Probability

• Publication date

  2009-02-02

• Fields of study

  Mathematics

• Identifiers
  DOI 10.1214/09-IMSCOLL511arXiv 0902.0333
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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