Generalized ridge estimation of a semiparametric regression model

We considered the following semiparametric regression model T y _i = X _i ^T β + s(t _i ) + e _i (i = 1,2,...,n). First, the generalized ridge estimators of both parameters and non-parameters are given without a restrained design matrix. Second, the generalized ridge estimator will be compared with the penalized least squares estimator under a mean squares error, and some conditions in which the former excels the latter are given. Finally, the validity and feasibility of the method is illustrated by a simulation example.