  Building on previous research of Chi and Chi (2022), the current paper
revisits estimation in robust structured regression under the
$\text{L}_2\text{E}$ criterion. We adopt the majorization-minimization (MM)
principle to design a new algorithm for updating the vector of regression
coefficients. Our sharp majorization achieves faster convergence than the
previous alternating proximal gradient descent algorithm (Chi and Chi, 2022).
In addition, we reparameterize the model by substituting precision for scale
and estimate precision via a modified Newton's method. This simplifies and
accelerates overall estimation. We also introduce distance-to-set penalties to
allow constrained estimation under nonconvex constraint sets. This tactic also
improves performance in coefficient estimation and structure recovery. Finally,
we demonstrate the merits of our improved tactics through a rich set of
simulation examples and a real data application.
