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

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.

Published in at http://dx.doi.org/10.1214/09-AOP467 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (4)

• Multivariate normal approximation using exchangeable pairs
• Translated Poisson approximation using exchangeable pair couplings
• Exchangeable pairs and Poisson approximation
• A note on the exchangeability condition in Stein's method

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