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Invariance and independence in multivariate distribution theory

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  • Dawid, A. P.

Abstract

Several general results are presented whereby various properties of independence or conditional independence between certain random variables may be deduced from the symmetries enjoyed by their joint distributions. These are applied to the distributions of sample correlation and canonical correlation coefficients when the underlying data-distribution has suitable orthogonal invariance. A typical result is that, for a random sample of observations on three independent normal variables, r12, r13, and r23.1 are mutually independent.

Suggested Citation

  • Dawid, A. P., 1985. "Invariance and independence in multivariate distribution theory," Journal of Multivariate Analysis, Elsevier, vol. 17(3), pages 304-315, December.
    • Handle: RePEc:eee:jmvana:v:17:y:1985:i:3:p:304-315
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    Cited by:

    1. Phillips, Peter C. B., 1988. "Conditional and unconditional statistical independence," Journal of Econometrics, Elsevier, vol. 38(3), pages 341-348, July.
    2. Jinfang Wang, 2010. "A universal algebraic approach for conditional independence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(4), pages 747-773, August.

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