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

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

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.

BIO: Vadim Gorin graduated from Moscow State University in 2008 and earned PhDs in Mathematics from both Moscow State University and Utrecht University in 2011. He moved to the United States in 2012 as a postdoctoral scholar at MSRI (now SLMath). Since then, he has held faculty positions at MIT, the University of Wisconsin-Madison, and the University of California, Berkeley, where he is currently jointly appointed in the Departments of Statistics and Mathematics.