Semiparametric model averaging prediction: a Bayesian approach

We present a novel model averaging method to construct a prediction function in semi-parametric form. The weighted sum of candidate semi-parametric models is taken as a prediction of the mean response. Marginal non-parametric regression models are approximated by spline basis functions and we apply a Bayesian Monte Carlo approach to fit such models. The optimal model weight parameters are estimated by minimising the least squares criterion with an explicit form. We implement our method in extensive simulation studies and illustrate its use with two real medical data examples. Our methods are demonstrated to be more accurate than both classical parametric model averaging methods and existing semi-parametric regression models.