Similar to variable selection in the linear regression model, selecting
significant components in the popular additive regression model is of great
interest. However, such components are unknown smooth functions of independent
variables, which are unobservable. As such, some approximation is needed. In
this paper, we suggest a combination of penalized regression spline
approximation and group variable selection, called the lasso-type spline method
(LSM), to handle this component selection problem with a diverging number of
strongly correlated variables in each group.

For consistency (even oracle properties) of estimation and model prediction,
almost all existing methods of variable/feature selection critically depend on
sparsity of models. However, for ``large $p$ and small $n$" models sparsity
assumption is hard to check and particularly, when this assumption is violated,
the consistency of all existing estimations is usually impossible because
working models selected by existing methods such as the LASSO and the Dantzig
selector are usually biased. To attack this problem, we in this paper propose
adaptive post-Dantzig estimation and model prediction.