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On Estimating the Dimensionality in Canonical Correlation Analysis

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  • Gunderson, Brenda K.
  • Muirhead, Robb J.
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    Abstract

    In canonical correlation analysis the number of nonzero population correlation coefficients is called the dimensionality. Asymptotic distributions of the dimensionalities estimated by Mallows's criterion and Akaike's criterion are given for nonnormal multivariate populations with finite fourth moments. These distributions have a simple form in the case of elliptical populations, and modified criteria are proposed which adjust for nonzero kurtosis. An estimation method based on a marginal likelihood function for the dimensionality is introduced and the asymptotic distribution of the corresponding estimator is derived for multivariate normal populations. It is shown that this estimator is not consistent, but that a simple modification yields consistency. An overall comparison of the various estimation methods is conducted through simulation studies.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 62 (1997)
    Issue (Month): 1 (July)
    Pages: 121-136

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    Handle: RePEc:eee:jmvana:v:62:y:1997:i:1:p:121-136

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    Related research

    Keywords: Akaike's information criterion canonical correlation coefficient dimensionality elliptical distribution kurtosis likelihood Mallows's criterion;

    References

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    1. Glynn, William J. & Muirhead, Robb J., 1978. "Inference in canonical correlation analysis," Journal of Multivariate Analysis, Elsevier, vol. 8(3), pages 468-478, September.
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    Cited by:
    1. Nielsen, Morten Orregaard & Shimotsu, Katsumi, 2007. "Determining the cointegrating rank in nonstationary fractional systems by the exact local Whittle approach," Journal of Econometrics, Elsevier, vol. 141(2), pages 574-596, December.
    2. Engle, Robert F. & Marcucci, Juri, 2006. "A long-run Pure Variance Common Features model for the common volatilities of the Dow Jones," Journal of Econometrics, Elsevier, vol. 132(1), pages 7-42, May.
    3. Robinson, Peter M. & Yajima, Yoshihiro, 2002. "Determination of cointegrating rank in fractional systems," Journal of Econometrics, Elsevier, vol. 106(2), pages 217-241, February.
    4. Willa Chen & Clifford Hurvich, 2004. "Semiparametric Estimation of Fractional Cointegrating Subspaces," Econometrics 0412007, EconWPA.

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