  We introduce flexible robust functional regression models, using various
heavy-tailed processes, including a Student $t$-process. We propose efficient
algorithms in estimating parameters for the marginal mean inferences and in
predicting conditional means as well interpolation and extrapolation for the
subject-specific inferences. We develop bootstrap prediction intervals for
conditional mean curves. Numerical studies show that the proposed model
provides robust analysis against data contamination or distribution
misspecification, and the proposed prediction intervals maintain the nominal
confidence levels. A real data application is presented as an illustrative
example.
