Conditional and Unconditional Statistical Independence
AbstractConditional 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.
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Bibliographic InfoPaper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 824R.
Length: 13 pages
Date of creation: 1987
Date of revision: Dec 1987
Publication status: Published in Journal of Econometrics (1988), 75(2): 341-348
Note: CFP 705.
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Other versions of this item:
- Phillips, Peter C. B., 1988. "Conditional and unconditional statistical independence," Journal of Econometrics, Elsevier, vol. 38(3), pages 341-348, July.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
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- Sokbae Lee & Oliver Linton & Yoon-Jae Whang, 2006. "Testing For Stochasticmonotonicity," STICERD - Econometrics Paper Series /2006/504, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
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- Oliver Linton & Pedro Gozalo, 1996. "Conditional Independence Restrictions: Testing and Estimation," Cowles Foundation Discussion Papers 1140, Cowles Foundation for Research in Economics, Yale University.
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