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

Group descent algorithms for nonconvex penalized linear and logistic regression models with grouped predictors