Multivariate Functional Regression Via Nested Reduced-Rank Regularization

We propose a nested reduced-rank regression (NRRR) approach in fitting model with multivariate functional responses and predictors to achieve tailored dimension reduction facilitate interpretation visualization. Our is based on two-level low-rank structure imposed the surfaces. A global identifies small set of latent principal that drives underlying association. local then controls complexity smoothness association between predictors. The problem boils down an integrated matrix approximation task through basis expansion, where blocks share some common row space and/or column space. This also finds potential applications time series modeling tensor regression. blockwise coordinate descent algorithm developed. establish consistency NRRR show nonasymptotic analysis it can at least comparable error rate Simulation studies demonstrate effectiveness NRRR. apply proposed methods electricity demand relate daily consumption trajectories temperatures. Supplementary files for this article are available online.