Estimating the parametric component of nonlinear partial spline model

Consider a nonlinear partial spline model Y = f ( β 0 , X ) + g 0 ( T ) + ϵ . This article studies the estimation problem of β 0 when g 0 is approximated by some graduating function. Some asymptotic results for β 0 are derived. In particular, it is shown that β 0 can be estimated with the usual parametric convergence rate without undersmoothing g 0 .