When we consider regression problem, there exist two approaches:
the parametric approach with a suitably chosen model including a finite dimensional parameter vector,
and the nonparametric approach without any assumption of structure.
The nonparametric approach has been known to be useful for regression problem,
which generally has consistency as an asymptotic property.
However the estimated structure with nonparametric approach is not easy to understand.
The parametric approach, on the other hand, does provide a nice interpretation of the estimated structure,
although it includes structural bias in general.
We propose a semiparametric penalized spline estimator which has a parametric structure as an initial guess.
The residual of parametric model is estimated nonparametrically by penalized spline method.
The interpretation of estimated structure by the proposed semiparametric estimator becomes clearer than that
by fully nonparametric estimator.
Furthermore it is shown that the asymptotic behavior of the proposed semiparametric estimator is almost similar
to the nonparametric penalized spline estimator.