  This paper studies some robust regression problems associated with the
$q$-norm loss ($q\ge1$) and the $\epsilon$-insensitive $q$-norm loss in the
reproducing kernel Hilbert space. We establish a variance-expectation bound
under a priori noise condition on the conditional distribution, which is the
key technique to measure the error bound. Explicit learning rates will be given
under the approximation ability assumptions on the reproducing kernel Hilbert
space.
