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The one-way Fubini property and conditional independence : an equivalence result
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Hammond, Peter J. and Sun, Yeneng (2016) The one-way Fubini property and conditional independence : an equivalence result. Discussion Paper. Coventry: University of Warwick. Department of Economics. CRETA Discussion Paper Series (22). (Unpublished)
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Official URL: http://www2.warwick.ac.uk/fac/soc/economics/resear...
Abstract
A general parameter process defined by a continuum of random variables is not jointly measurable with respect to the usual product σ-algebra. For the case of independent random variables, a one-way Fubini extension of the product space was constructed in [11] to satisfy a limited form of joint measurability. For the general case we show that this extension exists if and only if there is a countably generated σ-algebra given which the random variables are essentially pairwise conditionally independent, while their joint conditional distribution also satisfies a suitable joint measurability condition. Applications include new characterizations of essential pairwise independence and essential pairwise exchangeability through regular conditional distributions
with respect to the usual product σ-algebra in the framework of a
one-way Fubini extension.
Item Type: | Working or Discussion Paper (Discussion Paper) | ||||||
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Subjects: | Q Science > QA Mathematics | ||||||
Divisions: | Faculty of Social Sciences > Economics | ||||||
Library of Congress Subject Headings (LCSH): | Random variables | ||||||
Series Name: | CRETA Discussion Paper Series | ||||||
Publisher: | University of Warwick. Department of Economics | ||||||
Place of Publication: | Coventry | ||||||
Official Date: | April 2016 | ||||||
Dates: |
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Number: | 22 | ||||||
Number of Pages: | 17 | ||||||
Institution: | University of Warwick | ||||||
Status: | Not Peer Reviewed | ||||||
Publication Status: | Unpublished | ||||||
Access rights to Published version: | Restricted or Subscription Access | ||||||
Date of first compliant deposit: | 18 July 2019 | ||||||
Date of first compliant Open Access: | 18 July 2019 |
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