Detection of subcritical signals in CCA beyond spectral methods
Develop and analyze procedures for detecting and estimating subcritical signals in canonical correlation analysis—when the population squared canonical correlation ρ^2 lies below the spectral threshold 1/sqrt((τ_M−1)(τ_K−1))—particularly for non-Gaussian noise, for example via entrywise nonlinear transformations, and establish whether such methods can provably improve upon the spectral detectability threshold.
References
The details have not yet been figured out in the CCA setting, however, in the related PCA setup improvement can be achieved by applying a certain function (which depends on the distribution on the noise and is the identical function for the Gaussian noise --- leading to no improvements in the latter case) to each matrix element before using spectral methods, see, e.g., \citet{perry2018optimality} and references therein.