How weak are weak factors? Uniform inference for signal strength in signal plus noise models

Anna Bykhovskaya, Vadim Gorin and Sasha Sodin

Papers from arXiv.org

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.

Date: 2025-07
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-mac
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Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2507.18554

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