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On asymptotic distribution of maxima of complete and incomplete samples from stationary sequences

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  • Mladenovic, Pavle
  • Piterbarg, Vladimir

Abstract

Let (Xn) be a strictly stationary random sequence and Mn=max{X1,...,Xn}. Suppose that some of the random variables X1,X2,... can be observed and denote by the maximum of observed random variables from the set {X1,...,Xn}. We determine the limiting distribution of random vector under some condition of weak dependency which is more restrictive than the Leadbetter condition. An example concerning a storage process in discrete time with fractional Brownian motion as input is also given.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:116:y:2006:i:12:p:1977-1991
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    References listed on IDEAS

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    1. Hüsler, Jürg & Piterbarg, Vladimir, 2004. "Limit theorem for maximum of the storage process with fractional Brownian motion as input," Stochastic Processes and their Applications, Elsevier, vol. 114(2), pages 231-250, December.
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    Cited by:

    1. 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.
    2. Kudrov, Alexander, 2008. "Evaluation of the Distribution Function of Sample Maxima in Stationary Random Sequences with Pseudo-Stationary Trend," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 11(3), pages 64-86.
    3. 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.
    4. Alexandr V. Kudrov, 2013. "Extremal Quantiles Of Maximums For Stationary Sequences With Pseudo-Stationary Trend With Applications In Electricity Consumption," Montenegrin Journal of Economics, Economic Laboratory for Transition Research (ELIT), vol. 9(4), pages 53-64.
    5. 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.
    6. 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.
    7. Ferreira, Helena & Ferreira, Marta, 2015. "Extremes of scale mixtures of multivariate time series," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 82-99.
    8. Mladenovic, Pavle, 2009. "Maximum of a partial sample in the uniform AR(1) processes," Statistics & Probability Letters, Elsevier, vol. 79(11), pages 1414-1420, June.
    9. 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.
    10. 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.

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