Model Averaging Estimation for Sparse High-Dimensional Data

Studying model averaging for high-dimensional models with possibly sparse relevant covariates, we suggest a criterion for choosing weights. The resulting model averaging estimators of coefficients have a sparsity property and are asymptotically normal under certain regularity conditions. Furthermore, the proposed procedure is asymptotically optimal in the sense that its squared loss and risk are asymptotically identical to those of the best but infeasible model averaging estimator. Simulation experiments provide numerical evidence of these results.