IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v97y2006i5p1208-1220.html
   My bibliography  Save this article

Preserving multivariate dispersion: An application to the Wishart distribution

Author

Listed:
  • Fernández-Ponce, J.M.
  • Rodríguez-Griñolo, R.

Abstract

Univariate dispersive ordering has been extensively characterized by many authors over the last two decades. However, the multivariate version lacks extensive analysis. In this paper, sufficient and necessary conditions are given to preserve the strong multivariate dispersion order through properties of the corresponding transformation. Finally, these results are applied to the Wishart distribution which can be viewed as "the spread of the dispersion".

Suggested Citation

  • Fernández-Ponce, J.M. & Rodríguez-Griñolo, R., 2006. "Preserving multivariate dispersion: An application to the Wishart distribution," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1208-1220, May.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:5:p:1208-1220
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(05)00075-8
    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. Rojo, Javier & He, Guo Zhong, 1991. "New properties and characterizations of the dispersive ordering," Statistics & Probability Letters, Elsevier, vol. 11(4), pages 365-372, April.
    2. Bartoszewicz, Jaroslaw, 1995. "Stochastic order relations and the total time on test transform," Statistics & Probability Letters, Elsevier, vol. 22(2), pages 103-110, February.
    3. J. Bartoszewicz, 1985. "Moment inequalities for order statistics from ordered families of distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 32(1), pages 383-389, December.
    4. Oja, Hannu, 1983. "Descriptive statistics for multivariate distributions," Statistics & Probability Letters, Elsevier, vol. 1(6), pages 327-332, October.
    5. Giovagnoli, Alessandra & Wynn, H. P., 1995. "Multivariate dispersion orderings," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 325-332, March.
    6. Kochar, Subhash C., 1996. "Dispersive ordering of order statistics," Statistics & Probability Letters, Elsevier, vol. 27(3), pages 271-274, April.
    7. Bartoszewicz, J., 1987. "A note on dispersive ordering defined by hazard functions," Statistics & Probability Letters, Elsevier, vol. 6(1), pages 13-16, September.
    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. Ayala, Guillermo & López-Díaz, Miguel, 2009. "The simplex dispersion ordering and its application to the evaluation of human corneal endothelia," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1447-1464, August.

    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. Jongwoo Jeon & Subhash Kochar & Chul Park, 2006. "Dispersive ordering—Some applications and examples," Statistical Papers, Springer, vol. 47(2), pages 227-247, March.
    2. Ayala, Guillermo & López-Díaz, Miguel, 2009. "The simplex dispersion ordering and its application to the evaluation of human corneal endothelia," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1447-1464, August.
    3. Averous, Jean & Meste, Michel, 1997. "Median Balls: An Extension of the Interquantile Intervals to Multivariate Distributions," Journal of Multivariate Analysis, Elsevier, vol. 63(2), pages 222-241, November.
    4. Fernández-Ponce, J.M. & Pellerey, F. & Rodríguez-Griñolo, M.R., 2011. "A characterization of the multivariate excess wealth ordering," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 410-417.
    5. Carlos Carleos & Miguel López-Díaz, 2010. "A new family of dispersive orderings," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(2), pages 203-217, March.
    6. Belzunce, Félix & Ruiz, José M. & Suárez-Llorens, Alfonso, 2008. "On multivariate dispersion orderings based on the standard construction," Statistics & Probability Letters, Elsevier, vol. 78(3), pages 271-281, February.
    7. Ulysse Lawogni, 2019. "Measures of Inequality In Vectors Distributions," Working Papers hal-02377802, HAL.
    8. Volodina, Victoria & Wheatcroft, Edward & Wynn, Henry, 2022. "Comparing district heating options under uncertainty using stochastic ordering," LSE Research Online Documents on Economics 114292, London School of Economics and Political Science, LSE Library.
    9. 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.
    10. Giovagnoli, Alessandra & Wynn, H. P., 1995. "Multivariate dispersion orderings," Statistics & Probability Letters, Elsevier, vol. 22(4), pages 325-332, March.
    11. López-Díaz, Miguel, 2006. "An indexed multivariate dispersion ordering based on the Hausdorff distance," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1623-1637, August.
    12. Romanazzi, Mario, 2009. "Data depth, random simplices and multivariate dispersion," Statistics & Probability Letters, Elsevier, vol. 79(12), pages 1473-1479, June.
    13. Fernandez-Ponce, J. M. & Suarez-Llorens, A., 2003. "A multivariate dispersion ordering based on quantiles more widely separated," Journal of Multivariate Analysis, Elsevier, vol. 85(1), pages 40-53, April.
    14. José Pablo Arias‐Nicolás & Félix Belzunce & Olga Núñez‐Barrera & Alfonso Suárez‐Llorens, 2009. "A multivariate IFR notion based on the multivariate dispersive ordering," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(3), pages 339-358, May.
    15. G. Zioutas & C. Chatzinakos & T. D. Nguyen & L. Pitsoulis, 2017. "Optimization techniques for multivariate least trimmed absolute deviation estimation," Journal of Combinatorial Optimization, Springer, vol. 34(3), pages 781-797, October.
    16. Gangwei Cai & Baoping Zou & Xiaoting Chi & Xincheng He & Yuang Guo & Wen Jiang & Qian Wu & Yujin Zhang & Yanna Zhou, 2023. "Neighborhood Spatio-Temporal Impacts of SDG 8.9: The Case of Urban and Rural Exhibition-Driven Tourism by Multiple Methods," Land, MDPI, vol. 12(2), pages 1-37, January.
    17. Guillermo Ayala & María Concepción López-Díaz & Miguel López-Díaz & Lucía Martínez-Costa, 2015. "Methods and Algorithms to Test the Hausdorff and Simplex Dispersion Orders with an R Package," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 661-675, September.
    18. Satya R. Chakravarty & Pietro Muliere, 2003. "Welfare indicators: A review and new perspectives. 1. Measurement of inequality," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 457-497.
    19. Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Papers 1412.8434, arXiv.org, revised Sep 2015.
    20. Zhou, Xinyu & Ma, Yijia & Wu, Wei, 2023. "Statistical depth for point process via the isometric log-ratio transformation," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).

    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:97:y:2006:i:5:p:1208-1220. 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.