  Penalized regression is an attractive framework for variable selection
problems. Often, variables possess a grouping structure, and the relevant
selection problem is that of selecting groups, not individual variables. The
group lasso has been proposed as a way of extending the ideas of the lasso to
the problem of group selection. Nonconvex penalties such as SCAD and MCP have
been proposed and shown to have several advantages over the lasso; these
penalties may also be extended to the group selection problem, giving rise to
group SCAD and group MCP methods. Here, we describe algorithms for fitting
these models stably and efficiently. In addition, we present simulation results
and real data examples comparing and contrasting the statistical properties of
these methods.
