Joint limit distributions of exceedances point processes and partial sums of gaussian vector sequence |
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Authors: | Zuo Xiang Peng Jin Jun Tong Zhi Chao Weng |
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Affiliation: | 1. School of Mathematics and Statistics, Southwest University, Chongqing, 400715, P. R. China 2. Department of Actuarial Science, Faculty of Business and Economics, University of Lausanne, UNIL-Dorigny, 1015, Lausanne, Switzerland
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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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Keywords: | Multivariate Gaussian sequence exceedances point process partial sum order statistic joint limit distribution |
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