  This paper presents a model selection technique of estimation in
semiparametric regression models of the type
Y_i=\beta^{\prime}\underbarX_i+f(T_i)+W_i, i=1,...,n. The parametric and
nonparametric components are estimated simultaneously by this procedure.
Estimation is based on a collection of finite-dimensional models, using a
penalized least squares criterion for selection. We show that by tailoring the
penalty terms developed for nonparametric regression to semiparametric models,
we can consistently estimate the subset of nonzero coefficients of the linear
part. Moreover, the selected estimator of the linear component is
asymptotically normal.
