Conditional and Unconditional Statistical Independence

Peter Phillips

No 824R, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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.

Pages: 13 pages
Date: 1987, Revised 1987-12
Note: CFP 705.
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Published in Journal of Econometrics (1988), 75(2): 341-348

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