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On Estimating the Dimensionality in Canonical Correlation Analysis

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

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.

Suggested Citation

  • Gunderson, Brenda K. & Muirhead, Robb J., 1997. "On Estimating the Dimensionality in Canonical Correlation Analysis," Journal of Multivariate Analysis, Elsevier, vol. 62(1), pages 121-136, July.
  • Handle: RePEc:eee:jmvana:v:62:y:1997:i:1:p:121-136
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    References listed on IDEAS

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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. Robinson, Peter M. & Yajima, Yoshihiro, 2002. "Determination of cointegrating rank in fractional systems," Journal of Econometrics, Elsevier, vol. 106(2), pages 217-241, February.
    2. Jiasen Zheng & Lixing Zhu, 2021. "Determining the number of canonical correlation pairs for high-dimensional vectors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(4), pages 737-756, August.
    3. 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.
    4. Fujikoshi, Yasunori & Sakurai, Tetsuro, 2016. "High-dimensional consistency of rank estimation criteria in multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 149(C), pages 199-212.
    5. Willa Chen & Clifford Hurvich, 2004. "Semiparametric Estimation of Fractional Cointegrating Subspaces," Econometrics 0412007, University Library of Munich, Germany.
    6. 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.
    7. Wei Luo & Bing Li, 2016. "Combining eigenvalues and variation of eigenvectors for order determination," Biometrika, Biometrika Trust, vol. 103(4), pages 875-887.

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