A Mallows-type Model Averaging Estimator for the Varying-Coefficient Partially Linear Model

In the last decade, significant theoretical advances have been made in the area of frequentist model averaging (FMA); however, the majority of this work has emphasised parametric model setups. This paper considers FMA for the semiparametric varying-coefficient partially linear model (VCPLM), which has gained prominence to become an extensively used modeling tool in recent years. Within this context, we develop a Mallows-type criterion for assigning model weights and prove its asymptotic optimality. A simulation study and a real data analysis demonstrate that the FMA estimator that arises from this criterion is vastly preferred to information criterion score-based model selection and averaging estimators. Our analysis is complicated by the fact that the VCPLM is subject to uncertainty arising not only from the choice of covariates, but also whether the covariate should enter the parametric or nonparametric parts of the model.