A finite exchangeable sequence (xi(1), ..., xi(N)) 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/N Sigma(N)(i=1) delta(xi i). 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
Bissiri, P. (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, PIER GIOVANNI
2010
Abstract
A finite exchangeable sequence (xi(1), ..., xi(N)) 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/N Sigma(N)(i=1) delta(xi i). 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
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