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Extremes of locally stationary chi-square processes with trend

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  • Liu, Peng
  • Ji, Lanpeng

Abstract

Chi-square processes with trend appear naturally as limiting processes in various statistical models. In this paper we are concerned with the exact tail asymptotics of the supremum taken over (0,1) of a class of locally stationary chi-square processes with particular admissible trends. An important tool for establishing our results is a weak version of Slepian’s lemma for chi-square processes. Some special cases including squared Brownian bridge and Bessel process are discussed.

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  • Liu, Peng & Ji, Lanpeng, 2017. "Extremes of locally stationary chi-square processes with trend," Stochastic Processes and their Applications, Elsevier, vol. 127(2), pages 497-525.
    • Handle: RePEc:eee:spapps:v:127:y:2017:i:2:p:497-525
    DOI: 10.1016/j.spa.2016.06.016
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    References listed on IDEAS

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    1. Hüsler, J. & Piterbarg, V., 1999. "Extremes of a certain class of Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 83(2), pages 257-271, October.
    2. Jarusková, Daniela & Piterbarg, Vladimir I., 2011. "Log-likelihood ratio test for detecting transient change," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 552-559, May.
    3. Dëbicki, Krzysztof & Kisowski, Pawel, 2008. "A note on upper estimates for Pickands constants," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2046-2051, October.
    4. Jaromír Antoch & Daniela Jarušková, 2013. "Testing for multiple change points," Computational Statistics, Springer, vol. 28(5), pages 2161-2183, October.
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    Cited by:

    1. Piterbarg, Vladimir I. & Rodionov, Igor V., 2020. "High excursions of Bessel and related random processes," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 4859-4872.
    2. Andriy Olenko & Dareen Omari, 2020. "Reduction Principle for Functionals of Vector Random Fields," Methodology and Computing in Applied Probability, Springer, vol. 22(2), pages 573-598, June.
    3. Qiao, Wanli, 2021. "Extremes of locally stationary Gaussian and chi fields on manifolds," Stochastic Processes and their Applications, Elsevier, vol. 133(C), pages 166-192.
    4. Ji, Lanpeng & Liu, Peng & Robert, Stephan, 2019. "Tail asymptotic behavior of the supremum of a class of chi-square processes," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    5. Popivoda, Goran & Stamatović, Siniša, 2019. "On probability of high extremes of Gaussian fields with a smooth random trend," Statistics & Probability Letters, Elsevier, vol. 147(C), pages 29-35.

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