{"ID":2890991,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.18554","arxiv_id":"2507.18554","title":"How weak are weak factors? Uniform inference for signal strength in signal plus noise models","abstract":"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.","short_abstract":"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 unif...","url_abs":"https://arxiv.org/abs/2507.18554","url_pdf":"https://arxiv.org/pdf/2507.18554v2","authors":"[\"Anna Bykhovskaya\",\"Vadim Gorin\",\"Sasha Sodin\"]","published":"2025-07-24T16:23:11Z","proceeding":"stat.ME","tasks":"[\"stat.ME\",\"econ.EM\",\"math.PR\",\"math.ST\"]","methods":"[]","has_code":false}