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Extreme Value Asymptotics for Multivariate Renewal Processes

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  • Steinebach, Josef
  • Eastwood, Vera R.
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    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.

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    File URL: http://www.sciencedirect.com/science/article/B6WK9-45PVKB3-7/2/01f647547b7ec097634c878256a37916
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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 56 (1996)
    Issue (Month): 2 (February)
    Pages: 284-302

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    Handle: RePEc:eee:jmvana:v:56:y:1996:i:2:p:284-302

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    Related research

    Keywords: Extreme value asymptotics multivariate renewal process invariance principle strong approximation multidimensional Wiener process stationary Gaussian process Rayleigh process (null);

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    Cited by:
    1. Horváth, Lajos & Kokoszka, Piotr & Steinebach, Josef, 1999. "Testing for Changes in Multivariate Dependent Observations with an Application to Temperature Changes," Journal of Multivariate Analysis, Elsevier, vol. 68(1), pages 96-119, January.

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