An efficient iterative model averaging framework for ultrahigh-dimensional linear regression models with missing data

This paper addresses the prediction problem in linear regression models with ultrahigh-dimensional covariates and missing response data. Assuming a missing at random mechanism, we introduced a novel nonparametric multiple imputation method to handle missing response values. Based on these imputed responses, we proposed an efficient iterative model averaging method that integrates an iterative screening process within a model averaging framework. The weights for the candidate models were determined using the Bayesian information criterion, ensuring an optimal balance between model fit and complexity. The computational feasibility of the proposed approach stems from its iterative structure, which significantly reduces the computational burden compared to conventional methods. Under certain regularity conditions, we demonstrated that the proposed method effectively mitigates the risk of overfitting and yields consistent estimators for the regression coefficients. Simulation studies and a real-world data application illustrate the practical efficacy of the proposed approach, showing its superior performance in terms of predictive accuracy and flexibility when compared to several competing approaches.