Journal article
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.
- Publication status:
- Published
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- Publisher copy:
- 10.1214/09-AOP467
Authors
- Journal:
- Annals of Probability More from this journal
- Volume:
- 37
- Issue:
- 6
- Pages:
- 2150-2173
- Publication date:
- 2007-11-07
- DOI:
- ISSN:
-
0091-1798
- Language:
-
English
- Keywords:
- Pubs id:
-
pubs:97513
- UUID:
-
uuid:ecb04d30-a8fe-47de-8d09-29bf8d3be498
- Local pid:
-
pubs:97513
- Source identifiers:
-
97513
- Deposit date:
-
2012-12-19
- ARK identifier:
Terms of use
- Copyright date:
- 2007
- Notes:
-
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)
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