  In this paper we consider regression problems subject to arbitrary noise in
the operator or design matrix. This characterization appropriately models many
physical phenomena with uncertainty in the regressors. Although the problem has
been studied extensively for ordinary/total least squares, and via models that
implicitly or explicitly assume Gaussianity, less attention has been paid to
improving estimation for regression problems under general uncertainty in the
design matrix. To address difficulties encountered when dealing with
distributions of sums of random variables, we rely on the saddle point method
to estimate densities and form an approximate log-likelihood to maximize. We
show that the proposed method performs favorably against other classical
methods.
