Konstantopoulos, Takis and Yuan, Linglong ORCID: 0000-0002-7851-1631
(2019)
On the extendibility of finitely exchangeable probability measures.
Transactions of the American Mathematical Society, 371 (10).
pp. 7067-7092.
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Abstract
A length-$n$ random sequence $X_1,\ldots,X_n$ in a space $S$ is finitely exchangeable if its distribution is invariant under all $n!$ permutations of coordinates. Given $N > n$, we study the extendibility problem: when is it the case that there is a length-$N$ exchangeable random sequence $Y_1,\ldots, Y_N$ so that $(Y_1,\ldots,Y_n)$ has the same distribution as $(X_1,\ldots,X_n)$? In this paper, we give a necessary and sufficient condition so that, for given $n$ and $N$, the extendibility problem admits a solution. This is done by employing functional-analytic and measure-theoretic arguments that take into account the symmetry. We also address the problem of infinite extendibility. Our results are valid when $X_1$ has a regular distribution in a locally compact Hausdorff space $S$. We also revisit the problem of representation of the distribution of a finitely exchangeable sequence.
Item Type: | Article |
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Uncontrolled Keywords: | Exchangeable, finitely exchangeable, extendible, signed measure, set function, bounded linear functional, Hahn Banach, permutation, de Finetti, urn measure, symmetric, U-statistics |
Depositing User: | Symplectic Admin |
Date Deposited: | 09 Apr 2020 10:37 |
Last Modified: | 18 Jan 2023 23:56 |
DOI: | 10.1090/tran/7701 |
Related URLs: | |
URI: | https://livrepository.liverpool.ac.uk/id/eprint/3081322 |
Available Versions of this Item
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ON THE EXTENDIBILITY OF FINITELY EXCHANGEABLE PROBABILITY MEASURES. (deposited 07 Mar 2019 10:06)
- On the extendibility of finitely exchangeable probability measures. (deposited 09 Apr 2020 10:37) [Currently Displayed]