Estimating the parametric component of nonlinear partial spline model

Consider a nonlinear partial spline model Y=f(β0,X)+g0(T)+ϵ. This article studies the estimation problem of β0 when g0g0 is approximated by some graduating function. Some asymptotic results for β0 are derived. In particular, it is shown that β0 can be estimated with the usual parametric convergence rate without undersmoothing g0g0.