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A note on marginal and conditional independence

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  • Loperfido, Nicola
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    Abstract

    Some statistical models imply that two random vectors are marginally independent as well as being conditionally independent with respect to another random vector. When the joint distribution of the vectors is normal, canonical correlation analysis may lead to relevant simplifications of the dependence structure. A similar application can be found in elliptical models, where linear independence does not imply statistical independence. Implications for Bayes analysis of the general linear model are discussed.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 80 (2010)
    Issue (Month): 23-24 (December)
    Pages: 1695-1699

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    Handle: RePEc:eee:stapro:v:80:y:2010:i:23-24:p:1695-1699

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    Keywords: Bayes linear analysis Canonical correlation analysis Elliptical distributions Sylvester law of nullity Unrelated parameters;

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    1. Granger, C W J, 1969. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, Econometric Society, vol. 37(3), pages 424-38, July.
    2. Granger, C. W. J., 1980. "Testing for causality : A personal viewpoint," Journal of Economic Dynamics and Control, Elsevier, vol. 2(1), pages 329-352, May.
    3. Florens, Jean-Pierre & Mouchart, Michel, 1985. "A Linear Theory for Noncausality," Econometrica, Econometric Society, vol. 53(1), pages 157-75, January.
    4. Nanny Wermuth & D. R. Cox, 2004. "Joint response graphs and separation induced by triangular systems," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 687-717.
    5. Eichler, Michael, 2007. "Granger causality and path diagrams for multivariate time series," Journal of Econometrics, Elsevier, vol. 137(2), pages 334-353, April.
    6. Granger, C. W. J., 1988. "Some recent development in a concept of causality," Journal of Econometrics, Elsevier, vol. 39(1-2), pages 199-211.
    7. Hosoya, Yuzo, 1977. "On the Granger Condition for Non-Causality," Econometrica, Econometric Society, vol. 45(7), pages 1735-36, October.
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