
Accession Number : AD0766811
Title : A Note on Exchangeable Sequences.
Descriptive Note : Technical rept.,
Corporate Author : STANFORD UNIV CALIF DEPT OF STATISTICS
Personal Author(s) : Olshen,Richard
Report Date : 17 SEP 1973
Pagination or Media Count : 15
Abstract : If (X sub 1),(X sub 2),... is an exchangeable sequence taking values in a complete, separable metric space, then there is a random variable M such that: (i) given M, (X sub 1),(X sub 2),... are conditionally independent and identically distributed; (ii) if (X sub 1),(X sub 2),... are conditionally independent and identically distributed given the random object Y, then a version of M is measurable with respect to the sigmafield spanned by Y; (iii) the sigmafield spanned by M coincides as a measure algebra with the invariant, tail, and exchangeable sigmafields of the process (X sub 1),(X sub 2),... , even though none of the latter three is countably generated. (Author)
Descriptors : (*STATISTICAL ANALYSIS, THEOREMS), RANDOM VARIABLES, SEQUENCES(MATHEMATICS), MEASURE THEORY, SET THEORY, PERMUTATIONS
Subject Categories : Statistics and Probability
Distribution Statement : APPROVED FOR PUBLIC RELEASE