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

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  • Bissiri, Pier Giovanni

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.

Suggested Citation

  • Bissiri, Pier Giovanni, 2010. "Characterization of the law of a finite exchangeable sequence through the finite-dimensional distributions of the empirical measure," Statistics & Probability Letters, Elsevier, vol. 80(17-18), pages 1306-1312, September.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:17-18:p:1306-1312
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    References listed on IDEAS

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    1. Hansen, Ben & Pitman, Jim, 2000. "Prediction rules for exchangeable sequences related to species sampling," Statistics & Probability Letters, Elsevier, vol. 46(3), pages 251-256, February.
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