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On the representation theorem for exchangeable arrays

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  • 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
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    Citations

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    Cited by:

    1. 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.
    2. 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).
    3. Eric Auerbach, 2019. "Identification and Estimation of a Partially Linear Regression Model using Network Data," Papers 1903.09679, arXiv.org, revised Jun 2021.
    4. 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.
    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.

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