IDEAS home Printed from
   My bibliography  Save this article

Weighted Frechet means as convex combinations in metric spaces: Properties and generalized median inequalities


  • Ginestet, Cedric E.
  • Simmons, Andrew
  • Kolaczyk, Eric D.


In this short note, we study the properties of the weighted Frechet mean as a convex combination operator on an arbitrary metric space (Y,d). We show that this binary operator is commutative, non-associative, idempotent, invariant to multiplication by a constant weight and possesses an identity element. We also cover the properties of the weighted cumulative Frechet mean. These tools allow us to derive several types of median inequalities for abstract metric spaces that hold for both negative and positive Alexandrov spaces. In particular, we show through an example that these bounds cannot be improved upon in general metric spaces. For weighted Frechet means, however, such inequalities can solely be derived for weights equal to or greater than one. This latter limitation highlights the inherent difficulties associated with abstract-valued random variables.

Suggested Citation

  • Ginestet, Cedric E. & Simmons, Andrew & Kolaczyk, Eric D., 2012. "Weighted Frechet means as convex combinations in metric spaces: Properties and generalized median inequalities," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1859-1863.
  • Handle: RePEc:eee:stapro:v:82:y:2012:i:10:p:1859-1863
    DOI: 10.1016/j.spl.2012.06.001

    Download full text from publisher

    File URL:
    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

    1. David Balding & Pablo Ferrari & Ricardo Fraiman & Mariela Sued, 2009. "Limit theorems for sequences of random trees," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 302-315, August.
    Full references (including those not matched with items on IDEAS)


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

    Cited by:

    1. Antonio Irpino & Rosanna Verde, 2015. "Basic statistics for distributional symbolic variables: a new metric-based approach," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 9(2), pages 143-175, June.


    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:82:y:2012:i:10:p:1859-1863. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.