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Extreme Value Asymptotics for Multivariate Renewal Processes

✍ Scribed by Josef Steinebach; Vera R. Eastwood

Publisher: Elsevier Science
Year: 1996
Tongue: English
Weight: 499 KB
Volume: 56
Category: Article
ISSN: 0047-259X
DOI: 10.1006/jmva.1996.0015

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✦ Synopsis

For a sequence of partial sums of d-dimensional independent identically distributed random vectors a corresponding multivariate renewal process is defined componentwise. Via strong invariance together with an extreme value limit theorem for Rayleigh processes, a number of weak asymptotic results are established for the d-dimensional renewal process. Similar theorems for the estimated version of this process are also derived. These results are suggested to serve as simultaneous asymptotic testing devices for detecting changes in the multivariate setting.

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