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Conditional and Unconditional Statistical Independence

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Author Info
Peter C.B. Phillips () (Cowles Foundation, Yale University)

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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.

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Publisher Info
Paper provided by Cowles Foundation, Yale University in its series Cowles Foundation Discussion Papers with number 824R.

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Length: 13 pages
Date of creation: 1987
Date of revision: Dec 1987
Publication status: Published in Journal of Econometrics (1988), 75(2): 341-348
Handle: RePEc:cwl:cwldpp:824r

Note: CFP 705.
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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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References listed on IDEAS
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.:
  1. Ullah, Aman & Zinde-Walsh, Victoria, 1984. "On the Robustness of LM, LR, and W Tests in Regression Models," Econometrica, Econometric Society, vol. 52(4), pages 1055-66, July. [Downloadable!] (restricted)
  2. Phillips, Peter C B, 1984. "The Exact Distribution of LIML: I," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 25(1), pages 249-61, February. [Downloadable!] (restricted)
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  3. Peter C.B. Phillips & Joon Y. Park, 1986. "Statistical Inference in Regressions with Integrated Processes: Part 2," Cowles Foundation Discussion Papers 819R, Cowles Foundation, Yale University, revised Feb 1987. [Downloadable!]
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  4. Dawid, A. P., 1985. "Invariance and independence in multivariate distribution theory," Journal of Multivariate Analysis, Elsevier, vol. 17(3), pages 304-315, December. [Downloadable!] (restricted)
  5. Peter C.B. Phillips & Vassilis A. Hajivassiliou, 1987. "Bimodal t-Ratios," Cowles Foundation Discussion Papers 842, Cowles Foundation, Yale University. [Downloadable!]
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Cited by:
(explanations, 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.)

  1. Sokbae 'Simon' Lee & Oliver Linton & Yoon-Jae Whang, 2008. "Testing for stochastic monotonicity," CeMMAP working papers CWP21/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies. [Downloadable!]
    Other versions:
  2. Oliver Linton & Pedro Gozalo, 1996. "Conditional Independence Restrictions: Testing and Estimation," Cowles Foundation Discussion Papers 1140, Cowles Foundation, Yale University. [Downloadable!]
  3. Kyungchul Song, 2007. "Testing Conditional Independence via Rosenblatt Transforms," PIER Working Paper Archive 07-026, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania. [Downloadable!]
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