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

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.

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Notes

  1. For a definition of conditional independence see Kallenberg (1997, p.109).

  2. A sequence \(A=\{x_n\}_{n\ge 1}\subset E\) will always refer to a countable nonfinite subset of \(E\).

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Correspondence to Tomás Prieto-Rumeau.

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This research was supported by the Spanish Ministerio de Economía y Competitividad, Grant Number MTM2012-31393.

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Vélez, R., Prieto-Rumeau, T. Random assignment processes: strong law of large numbers and De Finetti theorem. TEST 24, 136–165 (2015). https://doi.org/10.1007/s11749-014-0396-0

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