IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v75y2005i1p11-17.html
   My bibliography  Save this article

Multiple maxima in multivariate samples

Author

Listed:
  • Hashorva, Enkelejd
  • Hüsler, Jürg

Abstract

Let {Xn,n[greater-or-equal, slanted]1} be a sequence of independent random vectors in , with common continuous distribution function F. For fixed n[greater-or-equal, slanted]2, we say that a multiple maximum occurs among the sample points X1,...,Xn if Mn=Xi for some i=1,...,n, with Mn the componentwise sample maximum. In this paper, we investigate the asymptotic behaviour (n-->[infinity]) of the probability of observing a multiple maximum by imposing an asymptotic tail condition on F.

Suggested Citation

  • Hashorva, Enkelejd & Hüsler, Jürg, 2005. "Multiple maxima in multivariate samples," Statistics & Probability Letters, Elsevier, vol. 75(1), pages 11-17, November.
    • Handle: RePEc:eee:stapro:v:75:y:2005:i:1:p:11-17
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(05)00205-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Gnedin, Alexander V., 1998. "Records from a multivariate normal sample," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 11-15, July.
    2. Enkelejd Hashorva & Jürg Hüsler, 2003. "On multivariate Gaussian tails," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 55(3), pages 507-522, September.
    3. Gnedin, A. V., 1993. "On Multivariate Extremal Processes," Journal of Multivariate Analysis, Elsevier, vol. 46(2), pages 207-213, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Stoev, Stilian & Wang, Yizao, 2019. "Exchangeable random partitions from max-infinitely-divisible distributions," Statistics & Probability Letters, Elsevier, vol. 146(C), pages 50-56.
    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. Hashorva Enkelejd, 2016. "Domination of sample maxima and related extremal dependence measures," Dependence Modeling, De Gruyter, vol. 6(1), pages 88-101, May.
    4. Hashorva, Enkelejd & Rullière, Didier, 2020. "Asymptotic domination of sample maxima," Statistics & Probability Letters, Elsevier, vol. 160(C).
    5. Clément Dombry & Michael Falk & Maximilian Zott, 2019. "On Functional Records and Champions," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1252-1277, September.

    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. Clément Dombry & Michael Falk & Maximilian Zott, 2019. "On Functional Records and Champions," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1252-1277, September.
    3. Hua, Lei, 2017. "On a bivariate copula with both upper and lower full-range tail dependence," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 94-104.
    4. Peter Tankov, 2014. "Tails of weakly dependent random vectors," Papers 1402.4683, arXiv.org, revised Jan 2016.
    5. Hashorva, Enkelejd & Hüsler, Jürg, 2002. "Remarks on compound Poisson approximation of Gaussian random sequences," Statistics & Probability Letters, Elsevier, vol. 57(1), pages 1-8, March.
    6. Tankov, Peter, 2016. "Tails of weakly dependent random vectors," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 73-86.
    7. Zdravko I. Botev & Robert Salomone & Daniel Mackinlay, 2019. "Fast and accurate computation of the distribution of sums of dependent log-normals," Annals of Operations Research, Springer, vol. 280(1), pages 19-46, September.
    8. Hashorva, Enkelejd, 2008. "Tail asymptotic results for elliptical distributions," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 158-164, August.
    9. Zdravko Botev & Michel Mandjes & Ad Ridder, 2015. "Tail Distribution of the Maximum of Correlated Gaussian Random Variables," Tinbergen Institute Discussion Papers 15-132/III, Tinbergen Institute.
    10. Enkelejd Hashorva & Didier Rullière, 2019. "Asymptotic Domination Of Sample Maxima," Working Papers hal-02277020, HAL.
    11. Remco Hofstad & Harsha Honnappa, 2019. "Large deviations of bivariate Gaussian extrema," Queueing Systems: Theory and Applications, Springer, vol. 93(3), pages 333-349, December.
    12. Z. I. Botev, 2017. "The normal law under linear restrictions: simulation and estimation via minimax tilting," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 125-148, January.
    13. Hashorva, Enkelejd & Rullière, Didier, 2020. "Asymptotic domination of sample maxima," Statistics & Probability Letters, Elsevier, vol. 160(C).
    14. Archil Gulisashvili & Peter Tankov, 2014. "Implied volatility of basket options at extreme strikes," Papers 1406.0394, arXiv.org.
    15. Gnedin, Alexander V., 1998. "Records from a multivariate normal sample," Statistics & Probability Letters, Elsevier, vol. 39(1), pages 11-15, July.
    16. Hashorva, Enkelejd, 2009. "Asymptotics for Kotz Type III elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 927-935, April.
    17. Rabovic, Renata & Cizek, Pavel, 2016. "Estimation of Spatial Sample Selection Models : A Partial Maximum Likelihood Approach," Other publications TiSEM 8a4b2e5d-6787-4685-8b9e-1, Tilburg University, School of Economics and Management.
    18. Hashorva, Enkelejd, 2005. "Extremes of asymptotically spherical and elliptical random vectors," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 285-302, June.
    19. 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.
    20. Hua, Lei & Joe, Harry, 2011. "Tail order and intermediate tail dependence of multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1454-1471, November.

    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:75:y:2005:i:1:p:11-17. 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.