IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v213y2024ics0167715224001421.html
   My bibliography  Save this article

Exact quantiles of Gaussian process extremes

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715224001421
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2024.110173?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cao, Guanqun & Wang, Li, 2018. "Simultaneous inference for the mean of repeated functional data," Journal of Multivariate Analysis, Elsevier, vol. 165(C), pages 279-295.
    2. Lachièze-Rey, Raphaël, 2019. "Bicovariograms and Euler characteristic of random fields excursions," Stochastic Processes and their Applications, Elsevier, vol. 129(11), pages 4687-4703.
    3. Hu, Qirui, 2024. "Change point analysis of functional variance function with stationary error," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    4. Cai, Leheng & Hu, Qirui, 2024. "Simultaneous inference and uniform test for eigensystems of functional data," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    5. Telschow, Fabian J.E. & Davenport, Samuel & Schwartzman, Armin, 2022. "Functional delta residuals and applications to simultaneous confidence bands of moment based statistics," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    6. Italo R. Lima & Guanqun Cao & Nedret Billor, 2019. "M-based simultaneous inference for the mean function of functional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 577-598, June.
    7. Jin Seo Cho & Peter C. B. Phillips & Juwon Seo, 2019. "Parametric Inference on the Mean of Functional Data Applied to Lifetime Income Curves," Working papers 2019rwp-153, Yonsei University, Yonsei Economics Research Institute.
    8. Gu, Lijie & Wang, Suojin & Yang, Lijian, 2021. "Smooth simultaneous confidence band for the error distribution function in nonparametric regression," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    9. Jin Seo Cho & Peter C. B. Phillips & Juwon Seo, 2022. "Parametric Conditional Mean Inference With Functional Data Applied To Lifetime Income Curves," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(1), pages 391-456, February.
    10. Li Cai & Lijie Gu & Qihua Wang & Suojin Wang, 2021. "Simultaneous confidence bands for nonparametric regression with missing covariate data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1249-1279, December.
    11. Ghiglietti, Andrea & Paganoni, Anna Maria, 2017. "Exact tests for the means of Gaussian stochastic processes," Statistics & Probability Letters, Elsevier, vol. 131(C), pages 102-107.
    12. 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.
    13. Wang, Bo & Xu, Aiping, 2019. "Gaussian process methods for nonparametric functional regression with mixed predictors," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 80-90.
    14. Wenbo V. Li & Ang Wei, 2012. "A Gaussian Inequality for Expected Absolute Products," Journal of Theoretical Probability, Springer, vol. 25(1), pages 92-99, March.
    15. Livio Corain & Viatcheslav Melas & Andrey Pepelyshev & Luigi Salmaso, 2014. "New insights on permutation approach for hypothesis testing on functional data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(3), pages 339-356, September.
    16. Kraus, David, 2019. "Inferential procedures for partially observed functional data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 583-603.
    17. Lijie Gu & Li Wang & Wolfgang Härdle & Lijian Yang, 2014. "A simultaneous confidence corridor for varying coefficient regression with sparse functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(4), pages 806-843, December.
    18. Liebl, Dominik, 2019. "Inference for sparse and dense functional data with covariate adjustments," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 315-335.
    19. Li Cai & Lisha Li & Simin Huang & Liang Ma & Lijian Yang, 2020. "Oracally efficient estimation for dense functional data with holiday effects," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(1), pages 282-306, March.
    20. Li Cai & Suojin Wang, 2021. "Global statistical inference for the difference between two regression mean curves with covariates possibly partially missing," Statistical Papers, Springer, vol. 62(6), pages 2573-2602, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:213:y:2024:i:c:s0167715224001421. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.