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November 2009 Multivariate normal approximation with Stein’s method of exchangeable pairs under a general linearity condition
Gesine Reinert, Adrian Röllin
Ann. Probab. 37(6): 2150-2173 (November 2009). DOI: 10.1214/09-AOP467

Abstract

In this paper we establish a multivariate exchangeable pairs approach within the framework of Stein’s method to assess distributional distances to potentially singular multivariate normal distributions. By extending the statistics into a higher-dimensional space, we also propose an embedding method which allows for a normal approximation even when the corresponding statistics of interest do not lend themselves easily to Stein’s exchangeable pairs approach. To illustrate the method, we provide the examples of runs on the line as well as double-indexed permutation statistics.

Citation

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Gesine Reinert. Adrian Röllin. "Multivariate normal approximation with Stein’s method of exchangeable pairs under a general linearity condition." Ann. Probab. 37 (6) 2150 - 2173, November 2009. https://doi.org/10.1214/09-AOP467

Information

Published: November 2009
First available in Project Euclid: 16 November 2009

zbMATH: 1200.62010
MathSciNet: MR2573554
Digital Object Identifier: 10.1214/09-AOP467

Subjects:
Primary: 60F05
Secondary: 62E17

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 6 • November 2009
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