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A Multivariate CLT for Local Dependence withn−1/2 log nRate and Applications to Multivariate Graph Related Statistics

✍ Scribed by Yosef Rinott; Vladimir Rotar

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 677 KB
Volume: 56
Category: Article
ISSN: 0047-259X
DOI: 10.1006/jmva.1996.0017

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✦ Synopsis

This paper concerns the rate of convergence in the central limit theorem for certain local dependence structures. The main goal of the paper is to obtain estimates of the rate in the multidimensional case. Certain one-dimensional results are also improved by using some more flexible characteristics of dependence. Assuming the summands are bounded, we obtain rates close to those for independent variables. As an application we study the rate of the normal approximation of certain graph related statistics which arise in testing equality of several multivariate distributions.