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On a representation theorem for finitely exchangeable random vectors
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory.
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Probability Theory. Johannes Gutenberg Univ Mainz, Inst Math, Staudingerweg 9, D-55099 Mainz, Germany..
2016 (English)In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 442, no 2, 703-714 p.Article in journal (Refereed) PublishedText
Abstract [en]

A random vector X = (X1, ... ,X-n) with the X-i taking values in an arbitrary measurable space (S, Sp) is exchangeable if its law is the same as that of (X-sigma(1), ... ,X-sigma(n)) for any permutation a. We give an alternative and shorter proof of the representation result (Jaynes [6] and Kerns and Szekely [9]) stating that the law of X is a mixture of product probability measures with respect to a signed mixing measure. The result is "finitistic" in nature meaning that it is a matter of linear algebra for finite S. The passing from finite S to an arbitrary one may pose some measure-theoretic difficulties which are avoided by our proof. The mixing signed measure is not unique (examples are given), but we pay more attention to the one constructed in the proof ("canonical mixing measure") by pointing out some of its characteristics. The mixing measure is, in general, defined on the space of probability measures on S; but for S =, one can choose a mixing measure on R-n.

Place, publisher, year, edition, pages
2016. Vol. 442, no 2, 703-714 p.
Keyword [en]
Signed measure, Measurable space, Point measure, Exchangeable, Symmetric, Homogeneous polynomial
National Category
Probability Theory and Statistics Mathematical Analysis
Identifiers
URN: urn:nbn:se:uu:diva-299017DOI: 10.1016/j.jmaa.2016.04.070ISI: 000377322700017OAI: oai:DiVA.org:uu-299017DiVA: diva2:948875
Funder
Knut and Alice Wallenberg FoundationSwedish Research Council, 2013-4688
Available from: 2016-07-14 Created: 2016-07-13 Last updated: 2016-07-14Bibliographically approved

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