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

par M. Vadim Gorin (California University - Berkeley)

vendredi 22 mai 2026, 11:00 → 12:15 Europe/Paris

Auditorium 4 (Toulouse School of Economics)

We discuss 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.