Document Type
Discussion Paper
Publication Date
1-1-1987
CFDP Number
824R
CFDP Revision Date
1987-12-01
CFDP Pages
14
Abstract
Conditional independence almost everywhere in the space of the conditioning variates does not imply unconditional independence, although it may well imply unconditional independence of certain functions of the variables. An example that is important in linear regression theory is discussed in detail. This involves orthogonal projections on random linear manifolds, which are conditionally independent but not unconditionally independent under normality. Necessary and sufficient conditions are obtained under which conditional independence does imply unconditional independence.
Recommended Citation
Phillips, Peter C.B., "Conditional and Unconditional Statistical Independence" (1987). Cowles Foundation Discussion Papers. 1067.
https://elischolar.library.yale.edu/cowles-discussion-paper-series/1067