Optimal Model Averaging for Single-Index Models With Divergent Dimensions

This paper offers a new approach to address the model uncertainty in (potentially) divergent-dimensional single-index models (SIMs).We propose a model-averaging estimator based on cross-validation, which allows the dimension of covariates and the number of candidate models to increase with the sample size.We show that when all candidate models are misspecified, our model-averaging estimator is asymptotically optimal with its squared loss asymptotically identical to that of the infeasible best possible averaging estimator.In a different situation where correct models are available in the model set, the proposed method assigns all weights to the correct models asymptotically.We also propose averaging regularized estimators and prescreening methods to deal with high-dimensional covariates.We illustrate the method via simulations and two empirical applications.