How weak are weak factors? Uniform inference for signal strength in signal plus noise models
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917244872687616 |
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| author | Bykhovskaya, Anna Gorin, Vadim Sodin, Sasha |
| author_facet | Bykhovskaya, Anna Gorin, Vadim Sodin, Sasha |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18554 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | How weak are weak factors? Uniform inference for signal strength in signal plus noise models Bykhovskaya, Anna Gorin, Vadim Sodin, Sasha Methodology Econometrics Probability Statistics Theory 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. |
| title | How weak are weak factors? Uniform inference for signal strength in signal plus noise models |
| topic | Methodology Econometrics Probability Statistics Theory |
| url | https://arxiv.org/abs/2507.18554 |