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Continuity of Gaussian extreme distributions

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  • Yang, Lijian

Abstract

Distribution continuity is established for extremes of Gaussian processes with bounded sample paths and positive variance or continuous sample paths over compact domain, and for multiparameter Brownian sheets. These results provide probabilistic support for global inference on unknown functions.

Suggested Citation

  • Yang, Lijian, 2025. "Continuity of Gaussian extreme distributions," Statistics & Probability Letters, Elsevier, vol. 216(C).
    • Handle: RePEc:eee:stapro:v:216:y:2025:i:c:s0167715224002438
    DOI: 10.1016/j.spl.2024.110274
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    References listed on IDEAS

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    1. Holger Dette & Natalie Neumeyer & Ingrid Van Keilegom, 2007. "A new test for the parametric form of the variance function in non‐parametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 903-917, November.
    2. 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.
    3. 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.
    4. Wang, Jiangyan & Gu, Lijie & Yang, Lijian, 2022. "Oracle-efficient estimation for functional data error distribution with simultaneous confidence band," Computational Statistics & Data Analysis, Elsevier, vol. 167(C).
    5. Yang, Lijian, 2024. "Exact quantiles of Gaussian process extremes," Statistics & Probability Letters, Elsevier, vol. 213(C).
    6. Kun Huang & Sijie Zheng & Lijian Yang, 2022. "Inference for dependent error functional data with application to event-related potentials," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(4), pages 1100-1120, December.
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