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Tail asymptotic behavior of the supremum of a class of chi-square processes

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  • Ji, Lanpeng
  • Liu, Peng
  • Robert, Stephan

Abstract

We analyze in this paper the supremum of a class of chi-square processes over non-compact intervals, which can be seen as a multivariate counterpart of the generalized weighted Kolmogorov–Smirnov statistic. The boundedness and the exact tail asymptotic behavior of the supremum are derived. As examples, the chi-square process generated from the Brownian bridge and the fractional Brownian motion are discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:154:y:2019:i:c:6
    DOI: 10.1016/j.spl.2019.07.001
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    References listed on IDEAS

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    1. 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.
    2. Cheng, Dan, 2016. "Excursion probability of certain non-centered smooth Gaussian random fields," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 883-905.
    3. R'emy Chicheportiche & Jean-Philippe Bouchaud, 2012. "Weighted Kolmogorov-Smirnov test: Accounting for the tails," Papers 1207.7308, arXiv.org, revised Oct 2012.
    4. 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.
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    Cited by:

    1. 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.

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