Anna Bykhovskaya, Vadim Gorin, Sasha Sodin
arXiv 24 Jul 2025 · Statistics — Methodology
arXiv:2507.18554 · PDF · DOI · OpenAlex · Extracted main text
The paper analyzes four classical signal-plus-noise models: the factor model, spiked sample covariance matrices, the sum of a Wigner matrix and a low-rank perturbation, and canonical correlation analysis with low-rank dependencies. The objective is to construct confidence intervals for the signal strength that are uniformly valid across all regimes - strong, weak, and critical signals. We demonstrate that traditional Gaussian approximations fail in the critical regime. Instead, we introduce a universal transitional distribution that enables valid inference across the entire spectrum of signal strengths. The approach is illustrated through applications in macroeconomics and finance.
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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. Onatski (2012) Asymptotics of the principal components estimator of large factor models with weakly influential factors | 0.961 | 9 | 5 | 89% |
| 2 | D. Paul (2007) Asymptotics of sample eigenstructure for a large dimensional spiked covariance model | 0.928 | 5 | 4 | 80% |
| 3 | M. Capitaine, C. Donati-Martin, and D. Féral (2012) Central limit theorems for eigenvalues of deformations of Wigner matrices | 0.928 | 5 | 3 | 80% |
| 4 | F. Benaych-Georges and R. R. Nadakuditi (2012) The singular values and vectors of low rank perturbations of large rectangular random matrices | 0.874 | 6 | 5 | 67% |
| 5 | J. Bai and S. Ng (2002) Determining the number of factors in approximate factor models | 0.874 | 5 | 2 | 100% |
| 6 | A. Bykhovskaya and V. Gorin (2025) High-dimensional canonical correlation analysis | 0.860 | 11 | 5 | 64% |
| 7 | J. Baik, G. Ben Arous, and S. Péché (2005) Phase transition of the largest eigenvalue for nonnull complex sample covariance matrices | 0.843 | 3 | 3 | 100% |
| 8 | I. M. Johnstone and D. Paul (2018) PCA in high dimensions: An orientation | 0.843 | 3 | 3 | 100% |
| 9 | A. Bloemendal and B. Virág (2013) Limits of spiked random matrices I | 0.811 | 4 | 2 | 100% |
| 10 | M. Mo (2012) Rank 1 real Wishart spiked model | 0.811 | 4 | 2 | 100% |
Showing the top 10 of 126 scored citations.