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Asymptotic Theory for Canonical Correlation Analysis

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  • Anderson, T. W.
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    Abstract

    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.

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    File URL: http://www.sciencedirect.com/science/article/B6WK9-45GMXDC-1/2/0a1d86390884eb311f1e07c556a2dfcb
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    Bibliographic Info

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

    Volume (Year): 70 (1999)
    Issue (Month): 1 (July)
    Pages: 1-29

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    Handle: RePEc:eee:jmvana:v:70:y:1999:i:1:p:1-29

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    Related research

    Keywords: canonical variates reduced rank regression maximum likelihood estimators test of rank.;

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    Cited by:
    1. 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.
    2. Eubank, R.L. & Hsing, Tailen, 2008. "Canonical correlation for stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1634-1661, September.
    3. 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.
    4. 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.
    5. 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.
    6. 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, vol. 61(4), pages 995-1017, December.
    7. 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.
    8. Zaka Ratsimalahelo, 2003. "Strongly Consistent Determination of the Rank of Matrix," Econometrics 0307007, EconWPA.
    9. Bura, Efstathia & Cook, R. Dennis, 2003. "Rank estimation in reduced-rank regression," Journal of Multivariate Analysis, Elsevier, vol. 87(1), pages 159-176, October.
    10. 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, vol. 56(2), pages 279-304, June.

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