Factor-Adjusted Model Averaging

We propose a model averaging method for high-dimensional regression with highly correlated covariates. We use a factor structure to model the covariate dependence, allowing the covariates to be decomposed into two uncorrelated or weakly correlated latent components: common factors and idiosyncratic components. The number of common factors is allowed to diverge. We average estimators from factor-adjusted candidate models with augmented predictors composed of estimated common factors and idiosyncratic components. We prove the asymptotic optimality in the sense of achieving the lowest squared loss and the consistency when correctly specified models exist in the model space. Numerical experiments and a real-data analysis illustrate the promising performance of the proposed method.