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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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

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

First available in Project Euclid: 16 November 2009

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Zentralblatt MATH identifier

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

Stein’s method multivariate normal approximation exchangeable pairs


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.

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