Optimal Local Model Averaging for Divergent-Dimensional Functional-Coefficient Regressions

This paper proposes a novel local model averaging estimator for divergent-dimensional functional-coefficient regressions, which selects optimal functional combination weights by minimizing a local leave-h-out forward-validation criterion. It is shown that the proposed leave-h-out forward-validation model averaging (FVMA) estimator is asymptotically optimal in the sense of achieving the lowest possible local squared error loss in a class of functional model averaging estimators, which is also extended to the ultra-high dimensional framework. The rate of the FVMA-based varying-weights converging to the optimal weights minimizing the expected local quadratic errors is derived. Besides, when correctly specified models are included in the candidate model set, the proposed FVMA asymptotically assigns all varying weights to the correctly specified models. Furthermore, a simulation study and an empirical application highlight the merits of the proposed FVMA estimator relative to a variety of popular estimators with constant model averaging weights and model selection.