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Asymptotic Theory for Canonical Correlation Analysis


  • Anderson, T. W.


The asymptotic distribution of the sample canonical correlations and coefficients of the canonical variates is obtained when the nonzero population canonical correlations are distinct and sampling is from the normal distribution. The asymptotic distributions are also obtained for reduced rank regression when one set of variables is treated as independent (stochastic or nonstochastic) and the other set as dependent. Earlier work is corrected.

Suggested Citation

  • Anderson, T. W., 1999. "Asymptotic Theory for Canonical Correlation Analysis," Journal of Multivariate Analysis, Elsevier, vol. 70(1), pages 1-29, July.
  • Handle: RePEc:eee:jmvana:v:70:y:1999:i:1:p:1-29

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    Cited by:

    1. An, Baiguo & Guo, Jianhua & Wang, Hansheng, 2013. "Multivariate regression shrinkage and selection by canonical correlation analysis," Computational Statistics & Data Analysis, Elsevier, vol. 62(C), pages 93-107.
    2. Marco Centoni & Gianluca Cubadda, 2015. "Common Feature Analysis of Economic Time Series: An Overview and Recent Developments," CEIS Research Paper 355, Tor Vergata University, CEIS, revised 05 Oct 2015.
    3. Eubank, R.L. & Hsing, Tailen, 2008. "Canonical correlation for stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1634-1661, September.
    4. Zaka Ratsimalahelo, 2003. "Strongly Consistent Determination of the Rank of Matrix," Econometrics 0307007, EconWPA.
    5. Gilbert, Scott & ZemcĂ­k, Petr, 2006. "Who's afraid of reduced-rank parameterizations of multivariate models? Theory and example," Journal of Multivariate Analysis, Elsevier, vol. 97(4), pages 925-945, April.
    6. Bura, Efstathia & Cook, R. Dennis, 2003. "Rank estimation in reduced-rank regression," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 159-176, October.
    7. Taskinen, Sara & Croux, Christophe & Kankainen, Annaliisa & Ollila, Esa & Oja, Hannu, 2006. "Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 359-384, February.
    8. Zaka Ratsimalahelo, 2003. "Strongly Consistent Determination of the Rank of Matrix," EERI Research Paper Series EERI_RP_2003_04, Economics and Econometrics Research Institute (EERI), Brussels.
    9. Marco Centoni & Gianluca Cubadda, 2011. "Modelling comovements of economic time series: a selective survey," Statistica, Department of Statistics, University of Bologna, vol. 71(2), pages 267-294.
    10. Ogasawara, Haruhiko, 2007. "Asymptotic expansions of the distributions of estimators in canonical correlation analysis under nonnormality," Journal of Multivariate Analysis, Elsevier, vol. 98(9), pages 1726-1750, October.
    11. Jacques Dauxois & Guy Nkiet & Yves Romain, 2004. "Linear relative canonical analysis of Euclidean random variables, asymptotic study and some applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(2), pages 279-304, June.
    12. Haruhiko Ogasawara, 2009. "Asymptotic expansions in the singular value decomposition for cross covariance and correlation under nonnormality," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(4), pages 995-1017, December.
    13. Yamada, Tomoya, 2013. "Asymptotic properties of canonical correlation analysis for one group with additional observations," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 389-401.
    14. 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.


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