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Asymptotic expansions of test statistics for dimensionality and additional information in canonical correlation analysis when the dimension is large

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  • Sakurai, Tetsuro

Abstract

This paper examines asymptotic expansions of test statistics for dimensionality and additional information in canonical correlation analysis based on a sample of size N=n+1 on two sets of variables, i.e., and . These problems are related to dimension reduction. The asymptotic approximations of the statistics have been studied extensively when dimensions p1 and p2 are fixed and the sample size N tends to infinity. However, the approximations worsen as p1 and p2 increase. This paper derives asymptotic expansions of the test statistics when both the sample size and dimension are large, assuming that and have a joint (p1+p2)-variate normal distribution. Numerical simulations revealed that this approximation is more accurate than the classical approximation as the dimension increases.

Suggested Citation

  • Sakurai, Tetsuro, 2009. "Asymptotic expansions of test statistics for dimensionality and additional information in canonical correlation analysis when the dimension is large," Journal of Multivariate Analysis, Elsevier, vol. 100(5), pages 888-901, May.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:5:p:888-901
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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.
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