Abstract
In multivariate analysis, canonical correlation analysis is a powerful tool to deal with the relationship between two random vectors. In this paper, we establish a functional relation between the sample canonical correlation matrix and a special noncentral Fisher matrix. And under the large-dimensional setting, i.e., the dimensions of the random vectors tend to infinity proportionally to the sample size, we develop a phase transition and a central limit theorem for the sample spiked eigenvalues of the noncentral Fisher matrix. By these results, we further derive the limits and fluctuations of the sample canonical correlation coefficients.
Dedicated to the great statistician C. R. Rao on his 100th birthday.
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Acknowledgements
Z. D. Bai was partially supported by NSFC (No. 12171198). Z. Q. Hou was partially supported by NSFC (No. 12101359). J. Hu was partially supported by NSFC (No. 12171078, 11971097). D. D. Jiang was partially supported by NSFC (No. 11971371) and Shaanxi Province Natural Science Foundation 2020JM-049.
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Bai, Z., Hou, Z., Hu, J., Jiang, D., Zhang, X. (2021). Limiting Canonical Distribution of Two Large-Dimensional Random Vectors. In: Arnold, B.C., Balakrishnan, N., Coelho, C.A. (eds) Methodology and Applications of Statistics. Contributions to Statistics. Springer, Cham. https://doi.org/10.1007/978-3-030-83670-2_10
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DOI: https://doi.org/10.1007/978-3-030-83670-2_10
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