A finite exchangeable sequence (ξ1,...,ξN) need not satisfy de Finetti's conditional representation, but there is a one-to-one relationship between its law and the law of its empirical measure, i.e. 1/NΣi=1Nδξi. The aim of this paper is to identify the law of a finite exchangeable sequence through the finite-dimensional distributions of its empirical measure. The problem will be approached by singling out conditions that are necessary and sufficient so that a family of finite-dimensional distributions provides a complete characterization of the law of the empirical measure. This result is applied to construct laws of finite exchangeable sequences. © 2010 Elsevier B.V.

Characterization of the law of a finite exchangeable sequence through the finite-dimensional distributions of the empirical measure

Bissiri P. G.
2010

Abstract

A finite exchangeable sequence (ξ1,...,ξN) need not satisfy de Finetti's conditional representation, but there is a one-to-one relationship between its law and the law of its empirical measure, i.e. 1/NΣi=1Nδξi. The aim of this paper is to identify the law of a finite exchangeable sequence through the finite-dimensional distributions of its empirical measure. The problem will be approached by singling out conditions that are necessary and sufficient so that a family of finite-dimensional distributions provides a complete characterization of the law of the empirical measure. This result is applied to construct laws of finite exchangeable sequences. © 2010 Elsevier B.V.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/709744
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