On the representation theorem for exchangeable arrays

Olav Kallenberg

Journal of Multivariate Analysis, 1989, vol. 30, issue 1, 137-154

Abstract: Aldous and Hoover have proved independently that an array X = (Xij, i, j [set membership, variant] ) of random variables is exchangeable under separate or joint permutations of rows and columns, iff a.s. Xij[reverse not equivalent]f([alpha], [xi]i, [eta]j, [xi]ij) or Xij[reverse not equivalent]f([alpha], [xi]i, [xi]j, [xi]ij), respectively, for some measurable function f: 4--> and some i.i.d. random variables [alpha], [xi]i, [eta]j, [xi]ij, i, j[set membership, variant], or [alpha], [xi]i, [xi]ij=[xi]ji, 1

Keywords: separate; joint; exchangeability; measure; preserving; transformations; shell; tail; [sigma]-fields; conditional; independence; orthogonal; expansions (search for similar items in EconPapers)
Date: 1989
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Citations: View citations in EconPapers (9)

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