LIKELIHOOD RATIOS AND A TRANSITION FROM GAUSSIAN TO TRACY-WIDOM
IAIN JOHNSTONE – STANFORD UNIVERSITY
The Tracy-Widom distribution has found broad use in statistical theory and application. We first review some of this, focusing first on Principal Components Analysis and the `spiked model’. When the spike signal is below the Baik-Ben Arous-Peche threshold, likelihood ratio tests for presence of a spike are more efficient than the largest eigenvalue in many settings of multivariate statistics. In recent work in a spiked Wigner model with Egor Klochkov, Alexei Onatski and Damian Pavlyshyn, we study the likelihood ratio test in the transition zone around the BBP threshold, making use of a connection with the spherical Sherrington-Kirkpatrick model and establishing a conjecture of Baik and Lee.