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Exceedances point processes in the plane of stationary Gaussian sequences with data missing

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  • Peng, Zuoxiang
  • Tong, Jinjun
  • Weng, Zhichao

Abstract

In this paper, we consider the weak convergence of exceedances point processes in the plane of complete and incomplete stationary Gaussian sequences under some weak dependence conditions. The main results are applied to derive the asymptotic joint distribution of location and height of maximum with data missing, and the joint asymptotic behavior of the location of the first high-level exceedance and the location of the maximum with data missing.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:149:y:2019:i:c:p:73-79
    DOI: 10.1016/j.spl.2019.01.022
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    References listed on IDEAS

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    1. Ferreira, H. & Scotto, M., 2002. "On the asymptotic location of high values of a stationary sequence," Statistics & Probability Letters, Elsevier, vol. 60(4), pages 475-482, December.
    2. Krajka, Tomasz, 2011. "The asymptotic behaviour of maxima of complete and incomplete samples from stationary sequences," Stochastic Processes and their Applications, Elsevier, vol. 121(8), pages 1705-1719, August.
    3. 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.
    4. Peng, Zuoxiang & Cao, Lunfeng & Nadarajah, Saralees, 2010. "Asymptotic distributions of maxima of complete and incomplete samples from multivariate stationary Gaussian sequences," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2641-2647, November.
    5. Panga, Zacarias & Pereira, Luísa, 2018. "On the maxima and minima of complete and incomplete samples from nonstationary random fields," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 124-134.
    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. Mladenovic, Pavle & Piterbarg, Vladimir, 2006. "On asymptotic distribution of maxima of complete and incomplete samples from stationary sequences," Stochastic Processes and their Applications, Elsevier, vol. 116(12), pages 1977-1991, December.
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    Cited by:

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    2. 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).

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