A partial spline approach for semiparametric estimation of varying-coefficient partially linear models

A semiparametric method based on smoothing spline is proposed for the estimation of varying-coefficient partially linear models. A simple and efficient method is proposed, based on a partial spline technique with a lower-dimensional approximation to simultaneously estimate the varying-coefficient function and regression parameters. For interval inference, Bayesian confidence intervals were obtained based on the Bayes models for varying-coefficient functions. The performance of the proposed method is examined both through simulations and by applying it to Boston housing data.