Optimal model averaging for partially linear models with missing response variables and error‐prone covariates

Abstract

We consider the problem of optimal model averaging for partially linear models when the responses are missing at random and some covariates are measured with error. A novel weight choice criterion based on the Mallows‐type criterion is proposed for the weight vector to be used in the model averaging. The resulting model averaging estimator for the partially linear models is shown to be asymptotically optimal under some regularity conditions in terms of achieving the smallest possible squared loss. In addition, the existence of a local minimizing weight vector and its convergence rate to the risk‐based optimal weight vector are established. Simulation studies suggest that the proposed model averaging method generally outperforms existing methods. As an illustration, the proposed method is applied to analyze an HIV‐CD4 dataset.