IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v94y2005i1p159-171.html
   My bibliography  Save this article

On the dependence structure of order statistics

Author

Listed:
  • Avérous, Jean
  • Genest, Christian
  • C. Kochar, Subhash

Abstract

Given a random sample from a continuous variable, it is observed that the copula linking any pair of order statistics is independent of the parent distribution. To compare the degree of association between two such pairs of ordered random variables, a notion of relative monotone regression dependence (or stochastic increasingness) is considered. Using this concept, it is proved that for i

Suggested Citation

  • Avérous, Jean & Genest, Christian & C. Kochar, Subhash, 2005. "On the dependence structure of order statistics," Journal of Multivariate Analysis, Elsevier, vol. 94(1), pages 159-171, May.
    • Handle: RePEc:eee:jmvana:v:94:y:2005:i:1:p:159-171
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(04)00042-9
    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. Takemi Yanagimoto & Masashi Okamoto, 1969. "Partial orderings of permutations and monotonicity of a rank correlation statistic," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 489-506, December.
    2. Khaledi, Baha-Eldin & Kochar, Subhash, 2000. "On dispersive ordering between order statistics in one-sample and two-sample problems," Statistics & Probability Letters, Elsevier, vol. 46(3), pages 257-261, February.
    3. Boland, Philip J. & Hollander, Myles & Joag-Dev, Kumar & Kochar, Subhash, 1996. "Bivariate Dependence Properties of Order Statistics," Journal of Multivariate Analysis, Elsevier, vol. 56(1), pages 75-89, January.
    4. Z. Fang & H. Joe, 1992. "Further developments on some dependence orderings for continuous bivariate distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(3), pages 501-517, September.
    5. Marco Scarsini, 1984. "On measures of concordance," Post-Print hal-00542380, HAL.
    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. Khaledi, Baha-Eldin & Kochar, Subhash, 2005. "Dependence orderings for generalized order statistics," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 357-367, July.
    2. Moshe Shaked & Miguel A. Sordo & Alfonso Suárez-Llorens, 2012. "Global Dependence Stochastic Orders," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 617-648, September.
    3. Dolati, Ali & Genest, Christian & Kochar, Subhash C., 2008. "On the dependence between the extreme order statistics in the proportional hazards model," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 777-786, May.
    4. Kochar, Subhash & Xu, Maochao, 2008. "A new dependence ordering with applications," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2172-2184, October.
    5. Fountain, Robert L. & Herman Jr., John R. & Rustvold, D. Leif, 2008. "An application of Kendall distributions and alternative dependence measures: SPX vs. VIX," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 469-472, April.
    6. Navarro, Jorge & Balakrishnan, N., 2010. "Study of some measures of dependence between order statistics and systems," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 52-67, January.
    7. Genest, Christian & Kochar, Subhash C. & Xu, Maochao, 2009. "On the range of heterogeneous samples," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1587-1592, September.
    8. Navarro, Jorge & Spizzichino, Fabio, 2010. "On the relationships between copulas of order statistics and marginal distributions," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 473-479, March.
    9. Antonia Castaño-Martínez & Gema Pigueiras & Georgios Psarrakos & Miguel A. Sordo, 2020. "Increasing concave orderings of linear combinations of order statistics with applications to social welfare," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(6), pages 699-712, August.
    10. Hu, Taizhong & Xie, Chaode, 2006. "Negative dependence in the balls and bins experiment with applications to order statistics," Journal of Multivariate Analysis, Elsevier, vol. 97(6), pages 1342-1354, July.
    11. Lebrun, Régis & Dutfoy, Anne, 2014. "Copulas for order statistics with prescribed margins," Journal of Multivariate Analysis, Elsevier, vol. 128(C), pages 120-133.

    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. Kochar, Subhash & Xu, Maochao, 2008. "A new dependence ordering with applications," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2172-2184, October.
    2. Dolati, Ali & Genest, Christian & Kochar, Subhash C., 2008. "On the dependence between the extreme order statistics in the proportional hazards model," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 777-786, May.
    3. Colangelo, Antonio, 2008. "A study on LTD and RTI positive dependence orderings," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2222-2229, October.
    4. Moshe Shaked & Miguel A. Sordo & Alfonso Suárez-Llorens, 2012. "Global Dependence Stochastic Orders," Methodology and Computing in Applied Probability, Springer, vol. 14(3), pages 617-648, September.
    5. Genest, Christian & Verret, François, 2002. "The TP2 ordering of Kimeldorf and Sampson has the normal-agreeing property," Statistics & Probability Letters, Elsevier, vol. 57(4), pages 387-391, May.
    6. Harry Joe, 2018. "Dependence Properties of Conditional Distributions of some Copula Models," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 975-1001, September.
    7. Denuit, Michel & Lambert, Philippe, 2005. "Constraints on concordance measures in bivariate discrete data," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 40-57, March.
    8. Antonio Dalessandro & Gareth W. Peters, 2020. "Efficient and Accurate Evaluation Methods for Concordance Measures via Functional Tensor Characterizations of Copulas," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1089-1124, September.
    9. Shyamal Ghosh & Prajamitra Bhuyan & Maxim Finkelstein, 2022. "On a bivariate copula for modeling negative dependence: application to New York air quality data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 31(5), pages 1329-1353, December.
    10. Navarro, Jorge & Balakrishnan, N., 2010. "Study of some measures of dependence between order statistics and systems," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 52-67, January.
    11. Colangelo Antonio, 2006. "Some Positive Dependence Orderings involving Tail Dependence," Economics and Quantitative Methods qf0601, Department of Economics, University of Insubria.
    12. Fabrizio Durante & Erich Klement & Carlo Sempi & Manuel Úbeda-Flores, 2010. "Measures of non-exchangeability for bivariate random vectors," Statistical Papers, Springer, vol. 51(3), pages 687-699, September.
    13. Plischke, Elmar & Borgonovo, Emanuele, 2019. "Copula theory and probabilistic sensitivity analysis: Is there a connection?," European Journal of Operational Research, Elsevier, vol. 277(3), pages 1046-1059.
    14. Zhuang, Weiwei & Yao, Junchao & Hu, Taizhong, 2010. "Conditional ordering of order statistics," Journal of Multivariate Analysis, Elsevier, vol. 101(3), pages 640-644, March.
    15. Khaledi, Baha-Eldin & Kochar, Subhash, 2005. "Dependence orderings for generalized order statistics," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 357-367, July.
    16. Edoardo Berton & Lorenzo Mercuri, 2021. "An Efficient Unified Approach for Spread Option Pricing in a Copula Market Model," Papers 2112.11968, arXiv.org, revised Feb 2023.
    17. Koen Decancq, 2014. "Copula-based measurement of dependence between dimensions of well-being," Oxford Economic Papers, Oxford University Press, vol. 66(3), pages 681-701.
    18. Jiří Dvořák & Tomáš Mrkvička, 2022. "Graphical tests of independence for general distributions," Computational Statistics, Springer, vol. 37(2), pages 671-699, April.
    19. Liebscher Eckhard, 2017. "Copula-Based Dependence Measures For Piecewise Monotonicity," Dependence Modeling, De Gruyter, vol. 5(1), pages 198-220, August.
    20. Juan-José Ganuza & José S. Penalva, 2005. "On Information and Competition in Private Value Auctions," Working Papers 158, Barcelona School of Economics.

    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:jmvana:v:94:y:2005:i:1:p:159-171. 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.