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High-Dimensional Canonical Correlation Analysis

Anna Bykhovskaya, Vadim Gorin

arXiv 28 Jun 2023 · Econometrics · 1 citations (OpenAlex)

arXiv:2306.16393 · PDF · DOI · OpenAlex · Extracted main text

Abstract

This paper studies high-dimensional canonical correlation analysis (CCA) with an emphasis on the vectors that define canonical variables. The paper shows that when two dimensions of data grow to infinity jointly and proportionally, the classical CCA procedure for estimating those vectors fails to deliver a consistent estimate. This provides the first result on the impossibility of identification of canonical variables in the CCA procedure when all dimensions are large. As a countermeasure, the paper derives the magnitude of the estimation error, which can be used in practice to assess the precision of CCA estimates. Applications of the results to cyclical vs. non-cyclical stocks and to a limestone grassland data set are provided.

Citation extraction

70
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104
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Most heavily cited references

The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.

ReferenceIntensityMentionsSectionsMain text
1F. Yang (2022) Limiting distribution of the sample canonical correlation coefficients of high-dimensional random vectors1.00054100%
2Z. Bao, J. Hu, G. Pan, and W. Zhou (2019) Canonical correlation coefficients of high-dimensional gaussian vectors: Finite rank case0.96911691%
3K. W. Wachter (1980) The limiting empirical measure of multiple discriminant ratios0.9416483%
4R. Gittins (1985) Canonical Analysis: A Review with Applications in Ecology0.73732100%
5I. M. Johnstone (2008) Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy-widom limits and rates of convergence0.64422100%
6E. Andreou, P. Gagliardini, E. Ghysels, and M. Rubin (2019) Inference in group factor models with an application to mixed-frequency data0.64422100%
7F. Benaych-Georges and R. R. Nadakuditi (2012) The singular values and vectors of low rank perturbations of large rectangular random matrices0.64422100%
8I. Choi, R. Lin, and Y. Shin (2021) Canonical correlation-based model selection for the multilevel factors0.64422100%
9N. Firoozye, V. Tan, and S. Zohren (2023) Canonical portfolios: Optimal asset and signal combination0.64422100%
10M. Franchi, I. Georgiev, and P. Paruolo (2023) Estimating the number of common trends in large T and N factor models via canonical correlations analysis0.64422100%

Showing the top 10 of 70 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

Citing paperIntensityMentionsSections
1Canonical correlation regression with noisy data0.40511