  We propose a multivariate functional responses low rank regression model with
possible high dimensional functional responses and scalar covariates. By
expanding the slope functions on a set of sieve basis, we reconstruct the basis
coefficients as a matrix. To estimate these coefficients, we propose an
efficient procedure using nuclear norm regularization. We also derive error
bounds for our estimates and evaluate our method using simulations. We further
apply our method to the Human Connectome Project neuroimaging data to predict
cortical surface motor task-evoked functional magnetic resonance imaging
signals using various clinical covariates to illustrate the usefulness of our
results.
