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Measures of Association for Hilbertian Subspaces and Some Applications

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  • Dauxois, Jacques
  • Nkiet, Guy Martial

Abstract

Measures of association are introduced for Hilbertian subspaces, that are defined by a few axioms and are shown to be symmetric nondecreasing functions of the canonical coefficients. When particular subspaces are considered, classical measures of association are obtained as particular cases. Moreover, the proposed framework allows one to introduce new approaches for measuring partial noncorrelation, partial independence and linear predictability of a stationary process.

Suggested Citation

  • Dauxois, Jacques & Nkiet, Guy Martial, 2002. "Measures of Association for Hilbertian Subspaces and Some Applications," Journal of Multivariate Analysis, Elsevier, vol. 82(2), pages 263-298, August.
    • Handle: RePEc:eee:jmvana:v:82:y:2002:i:2:p:263-298
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    References listed on IDEAS

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    1. Elliot Cramer & W. Nicewander, 1979. "Some symmetric, invariant measures of multivariate association," Psychometrika, Springer;The Psychometric Society, vol. 44(1), pages 43-54, March.
    2. Mohsen Pourahmadi & A. G. Miamee, 1992. "Computation Of Canonical Correlation Between Past And Future Of A Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(4), pages 345-351, July.
    3. K. L. Vaninskii & A. M. Yaglom, 1990. "Stationary Processes With A Finite Number Of Non‐Zero Canonical Correlations Between Future And Past," Journal of Time Series Analysis, Wiley Blackwell, vol. 11(4), pages 361-375, July.
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    Cited by:

    1. Shin, Hyejin, 2008. "An extension of Fisher's discriminant analysis for stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1191-1216, July.

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