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.
Bissiri P.G. (2010). Characterization of the law of a finite exchangeable sequence through the finite-dimensional distributions of the empirical measure. STATISTICS & PROBABILITY LETTERS, 80(17-18), 1306-1312 [10.1016/j.spl.2010.04.010].
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
