Limit distribution of the sum and maximum from multivariate Gaussian sequences |
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Authors: | Barry James |
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Institution: | Department of Mathematics and Statistics, University of Minnesota Duluth, 1117 University Drive, Duluth, MN 55812, USA |
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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. |
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Keywords: | primary 60E70 secondary 60F05 60G15 |
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