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 sigma-field spanned by Y; (iii) the sigma-field spanned by M coincides as a measure algebra with the invariant, tail, and exchangeable sigma-fields 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