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The Limit Properties of Maxima of Stationary Gaussian Sequences Subject to Random Replacing

Author

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  • Yuwei Li

    (Department of Mathematic, Zhejiang Normal University, Jinhua 321004, China
    College of Data Science, Jiaxing University, Jiaxing 314001, China)

  • Zhongquan Tan

    (College of Data Science, Jiaxing University, Jiaxing 314001, China)

Abstract

In applications, missing data may occur randomly and some relevant datum are often used to replace the missing ones. This article mainly explores the influence of the degree of dependence of stationary Gaussian sequences on the joint asymptotic distribution of the maximum of the Gaussian sequence and its maximum when the sequence is subject to random replacing.

Suggested Citation

  • Yuwei Li & Zhongquan Tan, 2023. "The Limit Properties of Maxima of Stationary Gaussian Sequences Subject to Random Replacing," Mathematics, MDPI, vol. 11(14), pages 1-14, July.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:14:p:3155-:d:1196776
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    References listed on IDEAS

    as
    1. Pavle Mladenović & Lenka Živadinović, 2015. "Uniform AR(1) Processes and Maxima on Partial Samples," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(12), pages 2546-2563, June.
    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. 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. Robert, C.Y., 2010. "On asymptotic distribution of maxima of stationary sequences subject to random failure or censoring," Statistics & Probability Letters, Elsevier, vol. 80(2), pages 134-142, January.
    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. 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.
    Full references (including those not matched with items on IDEAS)

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