Abstract
For Gaussian stationary triangular arrays, it is well known that the extreme values may occur in clusters. Here we consider the joint behaviors of the point processes of clusters and the partial sums of bivariate stationary Gaussian triangular arrays. For a bivariate stationary Gaussian triangular array, we derive the asymptotic joint behavior of the point processes of clusters and prove that the point processes and partial sums are asymptotically independent. As an immediate consequence of the results, one may obtain the asymptotic joint distributions of the extremes and partial sums. We illustrate the theoretical findings with a numeric example.
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Acknowledgements
The authors would like to thank the referees for careful reading and for their perceptive and useful comments which greatly improved the paper. We appreciate Professor Wan Tang for his fruitful discussions on this topic. **hui Guo gratefully acknowledges the financial support by the National Natural Science Foundation of China (grant no. 71991472). Yingyin Lu was supported by Nanchong Municipal Government-Universities Scientific Cooperation Project SXHZ045.
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Guo, J., Lu, Y. Joint behavior of point processes of clusters and partial sums for stationary bivariate Gaussian triangular arrays. Ann Inst Stat Math 75, 17–37 (2023). https://doi.org/10.1007/s10463-022-00832-8
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DOI: https://doi.org/10.1007/s10463-022-00832-8