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Joint limit distributions of exceedances point processes and partial sums of gaussian vector sequence

Type of publication Peer-reviewed
Publikationsform Original article (peer-reviewed)
Publication date 2012
Author Peng Z, Tong J.J., Weng Z.,
Project Extremal Behaviour of Random Scaling Models
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Original article (peer-reviewed)

Journal Acta Mathematica Sinica, English Series
Volume (Issue) 28(8)
Page(s) 1647 - 1662
Title of proceedings Acta Mathematica Sinica, English Series
DOI DOI: 10.1007/s10114-012-0001-yOnline First™

Abstract

In this paper, we study the joint limit distributions of point processes of exceedances and partial sums of multivariate Gaussian sequences and show that the point processes and partial sums are asymptotically independent under some mild conditions. As a result, for a sequence of standardized stationary Gaussian vectors, we obtain that the point process of exceedances formed by the sequence (centered at the sample mean) converges in distribution to a Poisson process and it is asymptotically independent of the partial sums. The asymptotic joint limit distributions of order statistics and partial sums are also investigated under different conditions
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