A Note on Exchangeable Sequences.
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)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 17, 1973
- Accession Number
- AD0766811
Entities
People
- Richard Olshen
Organizations
- Stanford University