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Exact quantiles of Gaussian process extremes

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  • Yang, Lijian

Abstract

Under nearly minimal conditions, continuity of extreme distribution function is established for both continuous Gaussian processes and finite Gaussian sequences, which entails existence of exact quantiles at any level. Also proved under simple conditions is strict monotonicity of extreme distribution functions that ensures uniqueness of exact quantiles at any level. These results provide convenient tools for developing statistical theory about global inference on functions.

Suggested Citation

  • Yang, Lijian, 2024. "Exact quantiles of Gaussian process extremes," Statistics & Probability Letters, Elsevier, vol. 213(C).
    • Handle: RePEc:eee:stapro:v:213:y:2024:i:c:s0167715224001421
    DOI: 10.1016/j.spl.2024.110173
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    References listed on IDEAS

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    1. Guanqun Cao & Lijian Yang & David Todem, 2012. "Simultaneous inference for the mean function based on dense functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(2), pages 359-377.
    2. Azaïs, Jean-Marc & Wschebor, Mario, 2008. "A general expression for the distribution of the maximum of a Gaussian field and the approximation of the tail," Stochastic Processes and their Applications, Elsevier, vol. 118(7), pages 1190-1218, July.
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    Cited by:

    1. Yang, Lijian, 2025. "Continuity of Gaussian extreme distributions," Statistics & Probability Letters, Elsevier, vol. 216(C).

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