IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v83y2002i2p303-323.html
   My bibliography  Save this article

Estimation under l1-Symmetry

Author

Listed:
  • Fourdrinier, Dominique
  • Lemaire, Anne-Sophie

Abstract

The estimation of the location parameter of an l1-symmetric distribution is considered. Specifically when a p-dimensional random vector has a distribution that is a mixture of uniform distributions on the l1-sphere, we investigate a general class of estimators of the form [delta]=X+g. Under the usual quadratic loss, domination of [delta] over X is obtained through the partial differential inequality 4 div g+2Xc[not partial differential]2g+ ||g||2[less-than-or-equals, slant]0 and a new superharmonicity-type-like notion adapted to the l1-context. Specifically the condition of l1-superharmonicity is that 2[Delta]f+Xc[backward difference]3f[less-than-or-equals, slant]0 and div [backward difference]3f[greater-or-equal, slanted]0 as compared to the usual (l2) condition [Delta]f[less-than-or-equals, slant]0.

Suggested Citation

  • Fourdrinier, Dominique & Lemaire, Anne-Sophie, 2002. "Estimation under l1-Symmetry," Journal of Multivariate Analysis, Elsevier, vol. 83(2), pages 303-323, November.
    • Handle: RePEc:eee:jmvana:v:83:y:2002:i:2:p:303-323
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(01)92057-3
    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. Ralescu, Stefan & Brandwein, Ann Cohen & Strawderman, William E., 1992. "Stein estimation for non-normal spherically symmetric location families in three dimensions," Journal of Multivariate Analysis, Elsevier, vol. 42(1), pages 35-50, July.
    2. Ann Brandwein & Stefan Ralescu & William Strawderman, 1993. "Shrinkage estimators of the location parameter for certain spherically symmetric distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(3), pages 551-565, September.
    3. Chou, Jine-Phone & Strawderman, William E., 1990. "Minimax estimation of means of multivariate normal mixtures," Journal of Multivariate Analysis, Elsevier, vol. 35(2), pages 141-150, November.
    4. Kuwana, Yoichi & Kariya, Takeaki, 1991. "LBI tests for multivariate normality in exponential power distributions," Journal of Multivariate Analysis, Elsevier, vol. 39(1), pages 117-134, October.
    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. Fourdrinier, Dominique & Strawderman, William E., 2016. "Stokes’ theorem, Stein’s identity and completeness," Statistics & Probability Letters, Elsevier, vol. 109(C), pages 224-231.
    2. He Kun & Strawderman William E., 2001. "Estimation In Spherically Symmetric Regression With Random Design," Statistics & Risk Modeling, De Gruyter, vol. 19(1), pages 41-50, January.
    3. Saralees Nadarajah, 2006. "Acknowledgement of Priority: the Generalized Normal Distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 33(9), pages 1031-1032.
    4. Kubokawa, Tatsuya & Marchand, Éric & Strawderman, William E., 2015. "On predictive density estimation for location families under integrated squared error loss," Journal of Multivariate Analysis, Elsevier, vol. 142(C), pages 57-74.
    5. Wolf-Dieter Richter, 2017. "Statistical reasoning in dependent p-generalized elliptically contoured distributions and beyond," Journal of Statistical Distributions and Applications, Springer, vol. 4(1), pages 1-25, December.
    6. Norbert Henze, 2002. "Invariant tests for multivariate normality: a critical review," Statistical Papers, Springer, vol. 43(4), pages 467-506, October.
    7. Kubokawa, Tatsuya & Marchand, Éric & Strawderman, William E., 2015. "On improved shrinkage estimators for concave loss," Statistics & Probability Letters, Elsevier, vol. 96(C), pages 241-246.
    8. Ghannam, Mai & Nkurunziza, Sévérien, 2023. "Tensor Stein-rules in a generalized tensor regression model," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    9. Marchand, Éric & Strawderman, William E., 2020. "On shrinkage estimation for balanced loss functions," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    10. Dominique Fourdrinier & Tatsuya Kubokawa & William E. Strawderman, 2023. "Shrinkage Estimation of a Location Parameter for a Multivariate Skew Elliptic Distribution," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 808-828, February.
    11. Tatsuya Kubokawa & Éric Marchand & William E. Strawderman, 2014. "On Improved Shrinkage Estimators for Concave Loss," CIRJE F-Series CIRJE-F-936, CIRJE, Faculty of Economics, University of Tokyo.
    12. Fourdrinier, Dominique & Marchand, Éric & Strawderman, William E., 2019. "On efficient prediction and predictive density estimation for normal and spherically symmetric models," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 18-25.
    13. Tatsuya Kubokawa & Éric Marchand & William E. Strawderman, 2014. "On Predictive Density Estimation for Location Families under Integrated L 2 and L 1 Losses," CIRJE F-Series CIRJE-F-935, CIRJE, Faculty of Economics, University of Tokyo.
    14. Fourdrinier Dominique & Lemaire Anne-Sophie, 2000. "ESTIMATION OF THE MEAN OF A e1-EXPONENTIAL MULTIVARIATE DISTRIBUTION," Statistics & Risk Modeling, De Gruyter, vol. 18(3), pages 259-274, March.
    15. L. Fattorini & C. Pisani, 2000. "Assessing multivariate normality on the "worst" sample configuration," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(1-2), pages 23-38.
    16. Boente, Graciela & Salibián Barrera, Matías & Tyler, David E., 2014. "A characterization of elliptical distributions and some optimality properties of principal components for functional data," Journal of Multivariate Analysis, Elsevier, vol. 131(C), pages 254-264.

    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:83:y:2002:i:2:p:303-323. 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.