Extreme Value Asymptotics for Multivariate Renewal Processes

Josef Steinebach and Vera R. Eastwood

Journal of Multivariate Analysis, 1996, vol. 56, issue 2, 284-302

Abstract: For a sequence of partial sums ofd-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 thed-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.

Keywords: Extreme; value; asymptotics; multivariate; renewal; process; invariance; principle; strong; approximation; multidimensional; Wiener; process; stationary; Gaussian; process; Rayleigh; process; (null) (search for similar items in EconPapers)
Date: 1996
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Citations: View citations in EconPapers (2)

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