The Annals of Probability

Multivariate normal approximation with Stein’s method of exchangeable pairs under a general linearity condition

Gesine Reinert and Adrian Röllin

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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.

Article information

Source
Ann. Probab., Volume 37, Number 6 (2009), 2150-2173.

Dates
First available in Project Euclid: 16 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.aop/1258380785

Digital Object Identifier
doi:10.1214/09-AOP467

Mathematical Reviews number (MathSciNet)
MR2573554

Zentralblatt MATH identifier
1200.62010

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 62E17: Approximations to distributions (nonasymptotic)

Keywords
Stein’s method multivariate normal approximation exchangeable pairs

Citation

Reinert, Gesine; Röllin, Adrian. Multivariate normal approximation with Stein’s method of exchangeable pairs under a general linearity condition. Ann. Probab. 37 (2009), no. 6, 2150--2173. doi:10.1214/09-AOP467. https://projecteuclid.org/euclid.aop/1258380785


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