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Random assignment processes: strong law of large numbers and De Finetti theorem

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  • Ricardo Vélez
  • Tomás Prieto-Rumeau

Abstract

In the framework of a random assignment process—which randomly assigns an index within a finite set of labels to the points of an arbitrary set—we study sufficient conditions for a strong law of large numbers and a De Finetti theorem. In particular, this yields a family of finite-valued nonexchangeable random variables that are conditionally independent given some other random variable, that is, they verify a De Finetti theorem. We show an application of the De Finetti theorem and the law of large numbers to an estimation problem. Copyright Sociedad de Estadística e Investigación Operativa 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:testjl:v:24:y:2015:i:1:p:136-165
    DOI: 10.1007/s11749-014-0396-0
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    References listed on IDEAS

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    1. Kallenberg, Olav, 1989. "On the representation theorem for exchangeable arrays," Journal of Multivariate Analysis, Elsevier, vol. 30(1), pages 137-154, July.
    2. Ricardo Vélez Ibarrola & Tomás Prieto-Rumeau, 2011. "De Finetti-type theorems for nonexchangeable 0–1 random variables," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 293-310, August.
    3. Aldous, David J., 1981. "Representations for partially exchangeable arrays of random variables," Journal of Multivariate Analysis, Elsevier, vol. 11(4), pages 581-598, December.
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