Abstract
Let denote the number of distinct values among the first n terms of an infinite exchangeable sequence of random variables . We prove for that the extreme points of the convex set of all possible laws of are those derived from i.i.d. sampling from discrete uniform distributions and the limit case with . We also consider the problem in higher dimensions and variants of the problem for finite exchangeable sequences and exchangeable random partitions.
Acknowledgments
Many thanks to my advisor Jim Pitman for suggesting this problem and providing invaluable guidance, to Yuri Yakubovich for his significant contributions, and to the referees for their insightful feedback and excellent suggestions.
Citation
Theodore Zhu. "The distribution of the number of distinct values in a finite exchangeable sequence." Electron. J. Probab. 27 1 - 25, 2022. https://doi.org/10.1214/22-EJP815
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