IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v160y2020ics0167715220300067.html
   My bibliography  Save this article

Asymptotic domination of sample maxima

Author

Listed:
  • Hashorva, Enkelejd
  • Rullière, Didier

Abstract

For a given random sample from some underlying multivariate distribution F we consider the domination of the component-wise maxima by some independent random vector W with distribution function G. We show that the probability that certain components of the sample maxima are dominated by the corresponding components of W can be approximated under the assumptions that both F and G are in the max-domain of attraction of some max-stable distribution functions. We study further some basic probabilistic properties of the dominated components of sample maxima by W.

Suggested Citation

  • Hashorva, Enkelejd & Rullière, Didier, 2020. "Asymptotic domination of sample maxima," Statistics & Probability Letters, Elsevier, vol. 160(C).
    • Handle: RePEc:eee:stapro:v:160:y:2020:i:c:s0167715220300067
    DOI: 10.1016/j.spl.2020.108703
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715220300067
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2020.108703?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Clément Dombry & Mathieu Ribatet & Stilian Stoev, 2018. "Probabilities of Concurrent Extremes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1565-1582, October.
    2. Gnedin, Alexander V., 1998. "Records from a multivariate normal sample," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 11-15, July.
    3. Hashorva, Enkelejd & Hüsler, Jürg, 2005. "Multiple maxima in multivariate samples," Statistics & Probability Letters, Elsevier, vol. 75(1), pages 11-17, November.
    4. Genest, Christian & Rivest, Louis-Paul, 1989. "A characterization of gumbel's family of extreme value distributions," Statistics & Probability Letters, Elsevier, vol. 8(3), pages 207-211, August.
    5. Stoev, Stilian & Wang, Yizao, 2019. "Exchangeable random partitions from max-infinitely-divisible distributions," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 50-56.
    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. Hashorva Enkelejd, 2016. "Domination of sample maxima and related extremal dependence measures," Dependence Modeling, De Gruyter, vol. 6(1), pages 88-101, May.
    2. Ismihan Bayramoglu, 2016. "On the records of multivariate random sequences," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(6), pages 725-747, August.
    3. Clément Dombry & Michael Falk & Maximilian Zott, 2019. "On Functional Records and Champions," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1252-1277, September.
    4. Enkelejd Hashorva & Didier Rullière, 2019. "Asymptotic Domination Of Sample Maxima," Working Papers hal-02277020, HAL.
    5. Hashorva, Enkelejd & Hüsler, Jürg, 2005. "Multiple maxima in multivariate samples," Statistics & Probability Letters, Elsevier, vol. 75(1), pages 11-17, November.
    6. Okhrin Ostap & Okhrin Yarema & Schmid Wolfgang, 2013. "Properties of hierarchical Archimedean copulas," Statistics & Risk Modeling, De Gruyter, vol. 30(1), pages 21-54, March.
    7. repec:hum:wpaper:sfb649dp2009-014 is not listed on IDEAS
    8. Einmahl, John & Segers, Johan, 2020. "Empirical Tail Copulas for Functional Data," Other publications TiSEM edc722e6-cc70-4221-87a2-8, Tilburg University, School of Economics and Management.
    9. Segers, J.J.J., 2004. "Non-Parametric Inference for Bivariate Extreme-Value Copulas," Discussion Paper 2004-91, Tilburg University, Center for Economic Research.
    10. Segers, J.J.J., 2004. "Non-Parametric Inference for Bivariate Extreme-Value Copulas," Other publications TiSEM 3e837d24-e733-407c-bfaa-f, Tilburg University, School of Economics and Management.
    11. H. N. Nagaraja & Pankaj K. Choudhary & N. Matalas, 2002. "Number of Records in a Bivariate Sample with Application to Missouri River Flood Data," Methodology and Computing in Applied Probability, Springer, vol. 4(4), pages 377-391, December.
    12. Dutfoy Anne & Parey Sylvie & Roche Nicolas, 2014. "Multivariate Extreme Value Theory - A Tutorial with Applications to Hydrology and Meteorology," Dependence Modeling, De Gruyter, vol. 2(1), pages 1-19, June.
    13. Fan Yang & Yi Zhang, 2024. "Asymptotics of Sum of Heavy-tailed Risks with Copulas," Papers 2411.09657, arXiv.org.
    14. Li, Haijun & Wu, Peiling, 2013. "Extremal dependence of copulas: A tail density approach," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 99-111.
    15. Mainik Georg & Rüschendorf Ludger, 2012. "Ordering of multivariate risk models with respect to extreme portfolio losses," Statistics & Risk Modeling, De Gruyter, vol. 29(1), pages 73-106, March.
    16. Ressel, Paul, 2011. "A revision of Kimberling's results -- With an application to max-infinite divisibility of some Archimedean copulas," Statistics & Probability Letters, Elsevier, vol. 81(2), pages 207-211, February.
    17. Hofert, Marius & Huser, Raphaël & Prasad, Avinash, 2018. "Hierarchical Archimax copulas," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 195-211.
    18. Yongzhao Chen & Ka Chun Cheung & Sheung Chi Phillip Yam & Fei Lung Yuen & Jia Zeng, 2023. "On the Diversification Effect in Solvency II for Extremely Dependent Risks," Risks, MDPI, vol. 11(8), pages 1-22, August.
    19. Bücher, Axel & Dette, Holger & Volgushev, Stanislav, 2012. "A test for Archimedeanity in bivariate copula models," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 121-132.
    20. Durieu, Olivier & Wang, Yizao, 2022. "Phase transition for extremes of a stochastic model with long-range dependence and multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 143(C), pages 55-88.
    21. Mai, Jan-Frederik, 2018. "Extreme-value copulas associated with the expected scaled maximum of independent random variables," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 50-61.

    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:160:y:2020:i:c:s0167715220300067. 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.