Abstract
It is a well-known fact that an exchangeable sequence has empirical distributions that form a reverse-martingale. This paper is devoted to the proof of the converse statement. As a byproduct of the proof for the binary case, we introduce and discuss the notion of two-coloring exchangeability.
Acknowledgments
The authors wish to thank Steffen L. Lauritzen and Ehud Lehrer for their contribution to this work. Ehud is also acknowledged for highlighting the connection between the two-coloring exchangeability property and the marginal problem discussed in Subsection 2.2. Finally, the authors wish to thank an anonymous reviewer for their careful reading and comments which significantly improved the content of the paper.
Citation
Martin Bladt. Dimitry Shaiderman. "On the characterization of exchangeable sequences through reverse-martingale empirical distributions." Electron. Commun. Probab. 28 1 - 11, 2023. https://doi.org/10.1214/23-ECP553
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