IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v30y1989i1p137-154.html
   My bibliography  Save this article

On the representation theorem for exchangeable arrays

Author

Listed:
  • Kallenberg, Olav

Abstract

Aldous and Hoover have proved independently that an array X = (Xij, i, j [set membership, variant] ) of random variables is exchangeable under separate or joint permutations of rows and columns, iff a.s. Xij[reverse not equivalent]f([alpha], [xi]i, [eta]j, [xi]ij) or Xij[reverse not equivalent]f([alpha], [xi]i, [xi]j, [xi]ij), respectively, for some measurable function f: 4--> and some i.i.d. random variables [alpha], [xi]i, [eta]j, [xi]ij, i, j[set membership, variant], or [alpha], [xi]i, [xi]ij=[xi]ji, 1

Suggested Citation

  • Kallenberg, Olav, 1989. "On the representation theorem for exchangeable arrays," Journal of Multivariate Analysis, Elsevier, vol. 30(1), pages 137-154, July.
    • Handle: RePEc:eee:jmvana:v:30:y:1989:i:1:p:137-154
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0047-259X(89)90092-4
    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.

    Citations

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


    Cited by:

    1. Eric Auerbach, 2019. "Identification and Estimation of a Partially Linear Regression Model using Network Data," Papers 1903.09679, arXiv.org, revised Jun 2021.
    2. Paolo Leonetti, 2018. "Finite Partially Exchangeable Laws Are Signed Mixtures of Product Laws," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 80(2), pages 195-214, August.
    3. Ricardo Vélez & Tomás Prieto-Rumeau, 2015. "Random assignment processes: strong law of large numbers and De Finetti theorem," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 136-165, March.
    4. Davezies, Laurent & D’Haultfœuille, Xavier & Guyonvarch, Yannick, 2022. "The Marcinkiewicz–Zygmund law of large numbers for exchangeable arrays," Statistics & Probability Letters, Elsevier, vol. 188(C).
    5. Nan Liu & Yanbo Liu & Yuya Sasaki, 2024. "Estimation and Inference for Causal Functions with Multiway Clustered Data," Papers 2409.06654, arXiv.org.
    6. Porta Mana, PierGianLuca, 2018. "Quantum theory within the probability calculus: a there-you-go theorem and partially exchangeable models," OSF Preprints m38x6, Center for Open Science.
    7. Olav Kallenberg, 1999. "Multivariate Sampling and the Estimation Problem for Exchangeable Arrays," Journal of Theoretical Probability, Springer, vol. 12(3), pages 859-883, July.
    8. Diegert, Paul & Jochmans, Koen, 2024. "Nonparametric Identification of Models for Dyadic Data”," TSE Working Papers 24-1574, Toulouse School of Economics (TSE).

    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:30:y:1989:i:1:p:137-154. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.