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

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

2007-11-07

arxiv.org/abs/0711.1082v3

Annals of Probability 2009, Vol. 37, No. 6, 2150-2173

Mathematics

Probability

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

Scientific paper

10.1214/09-AOP467

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.

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