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High-dimensional asymptotic expansions for the distributions of canonical correlations

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  • Fujikoshi, Yasunori
  • Sakurai, Tetsuro

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.

Suggested Citation

  • Fujikoshi, Yasunori & Sakurai, Tetsuro, 2009. "High-dimensional asymptotic expansions for the distributions of canonical correlations," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 231-242, January.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:1:p:231-242
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    References listed on IDEAS

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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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    Cited by:

    1. 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.

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