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Point processes of exceedances by Gaussian random fields with applications to asymptotic locations of extreme order statistics

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  • Liu, Huiyan
  • Tan, Zhongquan

Abstract

In this paper, we studied the limit properties of the point processes of exceedances by stationary dependent Gaussian random fields. Applying the obtained results, we investigated the asymptotic relations between the locations and heights of extreme order statistics for stationary dependent Gaussian random fields. It is shown that these asymptotic relations are not sensitive to the dependence of the Gaussian random fields.

Suggested Citation

  • Liu, Huiyan & Tan, Zhongquan, 2022. "Point processes of exceedances by Gaussian random fields with applications to asymptotic locations of extreme order statistics," Statistics & Probability Letters, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:stapro:v:189:y:2022:i:c:s0167715222001419
    DOI: 10.1016/j.spl.2022.109593
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    References listed on IDEAS

    as
    1. Tan, Zhongquan, 2013. "The limit theorems on extremes for Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 436-444.
    2. Luísa Pereira, 2018. "On the Asymptotic Locations of the Largest and Smallest Extremes of a Stationary Sequence," Journal of Theoretical Probability, Springer, vol. 31(2), pages 853-866, June.
    3. Peng, Zuoxiang & Tong, Jinjun & Weng, Zhichao, 2019. "Exceedances point processes in the plane of stationary Gaussian sequences with data missing," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 73-79.
    4. Aiping Hu & Zuoxiang Peng & Yongcheng Qi, 2009. "Joint behavior of point process of exceedances and partial sum from a Gaussian sequence," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(3), pages 279-295, November.
    5. Xiao, Jinghong & Wen, Yuechun & Tan, Zhongquan, 2019. "The limit properties of point processes of upcrossings in nonstationary strongly dependent Gaussian models," Statistics & Probability Letters, Elsevier, vol. 149(C), pages 38-46.
    6. Pereira, L., 2009. "The asymptotic location of the maximum of a stationary random field," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2166-2169, October.
    7. Tan, Zhongquan & Tang, Linjun, 2017. "On the maxima and sums of homogeneous Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 44-54.
    8. Luísa Pereira & Zhongquan Tan, 2017. "Almost Sure Convergence for the Maximum of Nonstationary Random Fields," Journal of Theoretical Probability, Springer, vol. 30(3), pages 996-1013, September.
    Full references (including those not matched with items on IDEAS)

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