Limit distribution of the sum and maximum from multivariate Gaussian sequences

Barry James, Kang James and Yongcheng Qi

Journal of Multivariate Analysis, 2007, vol. 98, issue 3, 517-532

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.

Keywords: Gaussian; process; Maximum; Sum; Stationary; sequence (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (5)

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