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

Pier Giovanni Bissiri

Statistics & Probability Letters, 2010, vol. 80, issue 17-18, 1306-1312

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. . 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.

Keywords: de; Finetti's; theorem; Finite; exchangeability; Empirical; measure; Finitely; additive; probabilities (search for similar items in EconPapers)
Date: 2010
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