arXiv 28 Jun 2023 · Econometrics · 1 citations (OpenAlex)
arXiv:2306.16393 · PDF · DOI · OpenAlex · Extracted main text
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.
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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.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | F. Yang (2022) Limiting distribution of the sample canonical correlation coefficients of high-dimensional random vectors | 1.000 | 5 | 4 | 100% |
| 2 | Z. Bao, J. Hu, G. Pan, and W. Zhou (2019) Canonical correlation coefficients of high-dimensional gaussian vectors: Finite rank case | 0.969 | 11 | 6 | 91% |
| 3 | K. W. Wachter (1980) The limiting empirical measure of multiple discriminant ratios | 0.941 | 6 | 4 | 83% |
| 4 | R. Gittins (1985) Canonical Analysis: A Review with Applications in Ecology | 0.737 | 3 | 2 | 100% |
| 5 | I. M. Johnstone (2008) Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy-widom limits and rates of convergence | 0.644 | 2 | 2 | 100% |
| 6 | E. Andreou, P. Gagliardini, E. Ghysels, and M. Rubin (2019) Inference in group factor models with an application to mixed-frequency data | 0.644 | 2 | 2 | 100% |
| 7 | F. Benaych-Georges and R. R. Nadakuditi (2012) The singular values and vectors of low rank perturbations of large rectangular random matrices | 0.644 | 2 | 2 | 100% |
| 8 | I. Choi, R. Lin, and Y. Shin (2021) Canonical correlation-based model selection for the multilevel factors | 0.644 | 2 | 2 | 100% |
| 9 | N. Firoozye, V. Tan, and S. Zohren (2023) Canonical portfolios: Optimal asset and signal combination | 0.644 | 2 | 2 | 100% |
| 10 | M. Franchi, I. Georgiev, and P. Paruolo (2023) Estimating the number of common trends in large T and N factor models via canonical correlations analysis | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 70 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Canonical correlation regression with noisy data | 0.405 | 1 | 1 |