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Identifiability of Exchangeable Sequences with Identically Distributed Partial Sums


 
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1. Title Title of document Identifiability of Exchangeable Sequences with Identically Distributed Partial Sums
 
2. Creator Author's name, affiliation, country Steven N. Evans; University of California at Berkeley
 
2. Creator Author's name, affiliation, country Xiaowen Zhou; University of California at Berkeley
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) exchangeability, de Finetti's theorem, characteristics function, Laplace transform, moment generating function
 
3. Subject Subject classification 60E10, 60G09
 
4. Description Abstract Consider two exchangeable sequences $(X_k)_{k \in N}$ and $(\hat{X}_k)_{k \in N}$ with the property that $S_n \equiv \sum_{k=1}^n X_k$ and $\hat{S}_n \equiv \sum_{k=1}^n \hat{X}_k$ have the same distribution for all $n \in N$. David Aldous posed the following question. Does this imply that the two exchangeable sequences have the same joint distributions? We give an example that shows the answer to Aldous' question is, in general, in the negative. On the other hand, we show that the joint distributions of an exchangeable sequence can be recovered from the distributions of its partial sums if the sequence is a countable mixture of i.i.d. sequences that are either nonnegative or have finite moment generating functions in some common neighbourhood of zero.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s)
 
7. Date (YYYY-MM-DD) 1999-02-22
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ecp.ejpecp.org/article/view/1000
 
10. Identifier Digital Object Identifier 10.1214/ECP.v4-1000
 
11. Source Journal/conference title; vol., no. (year) Electronic Communications in Probability; Vol 4
 
12. Language English=en
 
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