  Generalized additive partial linear models (GAPLMs) are appealing for model
interpretation and prediction. However, for GAPLMs, the covariates and the
degree of smoothing in the nonparametric parts are often difficult to determine
in practice. To address this model selection uncertainty issue, we develop a
computationally feasible model averaging (MA) procedure. The model weights are
data-driven and selected based on multifold cross-validation (CV) (instead of
leave-one-out) for computational saving. When all the candidate models are
misspecified, we show that the proposed MA estimator for GAPLMs is
asymptotically optimal in the sense of achieving the lowest possible
Kullback-Leibler loss. In the other scenario where the candidate model set
contains at least one correct model, the weights chosen by the multifold CV are
asymptotically concentrated on the correct models. As a by-product, we propose
a variable importance measure to quantify the importances of the predictors in
GAPLMs based on the MA weights. It is shown to be able to asymptotically
identify the variables in the true model. Moreover, when the number of
candidate models is very large, a model screening method is provided. Numerical
experiments show the superiority of the proposed MA method over some existing
model averaging and selection methods.

Methodology