Conditional and Unconditional Statistical Independence
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.
|Date of creation:||1987|
|Date of revision:||Dec 1987|
|Publication status:||Published in Journal of Econometrics (1988), 75(2): 341-348|
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Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 249-61, February.
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- Peter C.B. Phillips, 1982. "The Exact Distribution of LIML: I," Cowles Foundation Discussion Papers 658, Cowles Foundation for Research in Economics, Yale University.
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"Statistical Inference in Regressions with Integrated Processes: Part 2,"
Cambridge University Press, vol. 5(01), pages 95-131, April.
- Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 2," Cowles Foundation Discussion Papers 819R, Cowles Foundation for Research in Economics, Yale University, revised Feb 1987.
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