Optimal model averaging for semiparametric partially linear models with measurement errors

This paper is concerned with optimal model averaging procedure for semiparametric partially linear models where some covariates are subject to measurement error. We proposed a corrected semiparametric generalized least squares estimation for unknown parameters and nonparametric function, and developed a Mallows-type criterion for weight choice. The resulting model average estimator is shown to be asymptotically optimal in terms of achieving the smallest possible squared error under some regularity conditions. The simulation studies demonstrate that the proposed procedure is superior to traditional model selection and model averaging methods. Our approach is further applied to Ragweed Pollen Level data. •We propose a corrected semiparametric generalized least squares estimation.•We develop a Mallows-type criterion for weight choice.•Our model averaging estimators are asymptotically optimal.•Simulation results show that our method is significantly better than other methods.