Limit distribution of the sum and maximum from multivariate Gaussian sequences

Barry James, Kang James, Yongcheng Qi

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

In this paper we study the asymptotic joint behavior of the maximum and the partial sum of a multivariate Gaussian sequence. The multivariate maximum is defined to be the coordinatewise maximum. Results extend univariate results of McCormick and Qi. We show that, under regularity conditions, if the maximum has a limiting distribution it is asymptotically independent of the partial sum. We also prove that the maximum of a stationary sequence, when normalized in a special sense which includes subtracting the sample mean, is asymptotically independent of the partial sum (again, under regularity conditions). The limiting distributions are also obtained.

Original languageEnglish (US)
Pages (from-to)517-532
Number of pages16
JournalJournal of Multivariate Analysis
Volume98
Issue number3
DOIs
StatePublished - Mar 2007

Keywords

  • Gaussian process
  • Maximum
  • Stationary sequence
  • Sum

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