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High-dimensional asymptotic expansions for the distributions of canonical correlations

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  • Fujikoshi, Yasunori
  • Sakurai, Tetsuro
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    Abstract

    This paper examines asymptotic distributions of the canonical correlations between and with q [infinity] and c=p/n-->c0[set membership, variant][0,1), assuming that and have a joint (q+p)-variate normal distribution. An extended Fisher's z-transformation is proposed. Then, the asymptotic distributions are improved further by deriving their asymptotic expansions. Numerical simulations revealed that our approximations are more accurate than the classical approximations for a large range of p,q, and n and the population canonical correlations.

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    Bibliographic Info

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

    Volume (Year): 100 (2009)
    Issue (Month): 1 (January)
    Pages: 231-242

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    Handle: RePEc:eee:jmvana:v:100:y:2009:i:1:p:231-242

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    Related research

    Keywords: primary; 62H10 secondary; 62E20 Asymptotic distributions Canonical correlations Extended Fisher's z-transformation High-dimensional framework;

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    1. Raudys, Sarunas & Young, Dean M., 2004. "Results in statistical discriminant analysis: a review of the former Soviet Union literature," Journal of Multivariate Analysis, Elsevier, vol. 89(1), pages 1-35, April.
    2. James R. Schott, 2005. "Testing for complete independence in high dimensions," Biometrika, Biometrika Trust, vol. 92(4), pages 951-956, December.
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