arXiv 23 Nov 2024 · Statistics — Methodology · 1 citations (OpenAlex)
arXiv:2411.15625 · PDF · DOI · OpenAlex · Extracted main text
For over a century canonical correlations, variables, and related concepts have been studied across various fields, with contributions dating back to Jordan [1875] and Hotelling [1936]. This text surveys the evolution of canonical correlation analysis, a fundamental statistical tool, beginning with its foundational theorems and progressing to recent developments and open research problems. Along the way we introduce and review methods, notions, and fundamental concepts from linear algebra, random matrix theory, and high-dimensional statistics, placing particular emphasis on rigorous mathematical treatment. The survey is intended for technically proficient graduate students and other researchers with an interest in this area. The content is organized into five chapters, supplemented by six sets of exercises found in Chapter 6. These exercises introduce additional material, reinforce key concepts, and serve to bridge ideas across chapters. We recommend the following sequence: first, solve Problem Set 0, then proceed with Chapter 1, solve Problem Set 1, and so on through the text.
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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 | A. Bykhovskaya and V. Gorin (2023) High-dimensional canonical correlation analysis | 0.874 | 8 | 2 | 100% |
| 2 | A. Bykhovskaya and V. Gorin (2022) Cointegration in large VARs | 0.874 | 7 | 2 | 100% |
| 3 | P. Forrester (2010) Log-gases and random matrices | 0.874 | 5 | 2 | 100% |
| 4 | A. Bykhovskaya and V. Gorin (2024) Asymptotics of cointegration tests for high-dimensional VAR($k$) | 0.737 | 3 | 2 | 100% |
| 5 | P. D. Lax (2007) Linear Algebra and Its Applications | 0.737 | 3 | 2 | 100% |
| 6 | R. J. Muirhead (2009) Aspects of multivariate statistical theory | 0.737 | 3 | 2 | 100% |
| 7 | H. Hotelling (1936) Relations between two sets of variates | 0.644 | 2 | 2 | 100% |
| 8 | R. A. Horn and C. R. Johnson (2012) Matrix analysis | 0.644 | 2 | 2 | 100% |
| 9 | P. Hsu (1941) On the limiting distribution of the canonical correlations | 0.644 | 2 | 2 | 100% |
| 10 | S. Johansen (1995) Likelihood-based inference in cointegrated vector autoregressive models | 0.644 | 2 | 2 | 100% |
Showing the top 10 of 83 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 |